Rav Avrohom Yitzchok HaKohen Kook, Zatzal: The Perspective of the Chofetz Chaim, Zatzal
Rav Aharon HaKohen, the son-in-law of the Chofetz Chaim, wrote the following in 1928:
My father-in-law very much esteemed and loved [“HaMokir U’Mechaveiv M’od”] Rav Kook, and his soul was very pained [“Da’avah M’od”] when he heard about those who sought to persecute him [“Odos HaRedifos Alav”].
From Igros LaRAYaH, #30
Rav Hershel Schachter: The Perspectives of HaGaon Rav David Lifshitz, Zatzal, and HaGaon Rav Pinchas Hirschprung, Zatzal
HaGaon Rav David Lifshitz, Zatzal, and HaGaon Rav Pinchas Hirschsprung, Zatzal, wrote approbations ["haskamos"] for one or more of Rav Hershel Schachter’s works. Here are translated excerpts:
Rav Lifshitz [haskama to Eretz HaTzvi]
"My friend, the consummate Torah-scholar [‘Yedidi, HaRav HaGaon’], Rabbi Hershel Schachter, may he live a long and good life [‘Shlita’], informed me of the good news [‘Hishmee’ani Tovos B’Baseiro’]" that he is publishing a work of Torah-scholarship. "As for me, how dear is HaRav HaGaon Shlita, for I know him from when he was a youth as a distinguished student in in our yeshiva [and] and he showed with great clarity that he was destined for greatness [‘Her’ah B’Alil She-No’ad L’Gadlus’], as we understood the case to be [that he would achieve Gadlus], so have we seen…" Rav Lifshitz explains that he did not have time to examine the work in its entirety, but nonetheless, he states, "We can presume that his words will generate joy and wisdom, illuminating the eyes and refreshing the spirit…"
Rav Hirschprung [haskama to B’Ikvei HaTzon]
"Rabbi Hershel Schachter, the distinguished consummate Torah-scholar [‘HaGaon HaMuvhak’] sent me his work for an approbation…I was amazed [‘Hishtomamti’] at the largesse of the breadth of his knowledge in all aspects of Torah-scholarship and at his many well-predicated novellae."
The Bostoner Rebbe, Shlita, on Reb David Hatuel and his Kehillah
"There are people like David Hatuel who live the life of a tzaddik–‘Ve’tzaddik be’emunaso yichyeh.’ We must not disregard any group (or individual) because they do not understand the mitzvah of yishuv Eretz Yisrael the same way we do. We certainly must not disrespect any group that contains such an outstanding Jew as David Hatuel just because their dress, while conforming to the halachas of tznius, is different from ours. The main factor must be the emunah shleimah."
"We must understand that what they are doing is not done for any financial profit or out of the ‘kochi ve’otsem yodi’ of the founding Zionists, which was not based on any shred of emunah. We must understand our neighbors, their motivations and their goals. When we are told not to judge our friend until we reach his position, it means until we really understand his fundamental outlook and what drives him, and not merely what we think of him."
from "Immeasurable Faith Amidst Unspeakable Tragedy," by the Bostoner Rebbe, Shlita, in Jewish Press, May 2004
The Rav, Zatzal: The Perspectives of Rav Moshe, Zatzal, and HaGaon Rav Mordechai Gifter, Zatzal
In 1983, the Student Organization of Yeshiva University published a volume of Torah works to honor the Rav, Zatzal, on his 80th birthday. It was entitled, K’vod HaRav. The volume contained works by Torah-scholars from within and without Yeshiva University. Among these works was a teshuvah (responsum) from Rav Moshe, Zatzal, and a chibbur (article) from HaGaon Rav Mordechai Gifter, Zatzal. The following is a translation of what Rav Moshe and Rav Gifter wrote as prefaces to their respective pieces:
Rav Moshe:
“I am writing now (‘Basi B’Zeh‘) to send my blessing to the editors of the Jubilee volume that the students of the great consummate Torah-scholar, our teacher, Rav Yosef Dov Soloveitchik, may he live a long and good life (‘HaGaon HaGadol Moreinu HaRav Yosef Dov Soloveitchik Shlita‘), arranged in his honor, to mark his 80th birthday. And [I also write] to express my prayer that G-d lengthen the days and years of my great friend, with a good ‘old age, vigorous and fresh they shall be,’ and that he should continue to disseminate Torah publicly and to occupy himself with the needs of the community, for the sake of the honor of G-d and His Torah, and for the splendor (‘Tif’eres’) of our families. With friendship and esteem (’Hukra‘), Moshe Feinstein.”
Rav Gifter:
“Upon the reaching of the age of 80 by the Rosh Yeshiva, HaGaon Rav Yosef Dov HaLevi Soloveitchik, Shlita, I remember his arrival in the United States and his father’s joy–my mentor, HaGaon Rav Moshe Soloveitchik, Zatzal–with a wise son that brings joy to his father…Upon his reaching the age of 80, may G-d strengthen him so that he can continue to disseminate Torah and to develop students who understand the Torah…”
The Rav, Zatzal, and HaGaon Rav Aharon Kotler, Zatzal
These passages are from "A Fire In His Soul," which is the biography of the great Oskan B’Tzorchei Tzibbur, Reb Irving Bunim, Z"L, written by his son, Rav Amos, Shlita. Rav Bunim sheds a great a deal of light on the relationship between HaGaonim Rav Aharon Kotler and Rav Yosef Dov HaLevi Soloveitchik, Zichronom L’Veracha.
["Bunim" here always refers to Reb Irving and "the Rosh Yeshiva" here always refers to Rav Kotler.]
p.211
"Bunim saw that the Rosh Yeshiva always distinguished between people and the principles they professed. Bunim never saw him attack another Jew, except for those who negated the Torah. A person’s opinion might be at fault, Rabbi Kotler said, but never the person. Rabbi Kotler could disagree vehemently with a fellow gadol’s opinion while respecting him for his Torah knowledge and middos."
p.212
"[Rav Kotler] differed with Rabbi Joseph B. Soloveitchick’s approval of secular education and secular Zionism. Still, Rabbi Kotler invited Rabbi Soloveitchik to be honorary chairman of Chinuch Atzmai’s first annual dinner. During his speech, Rabbi Soloveitchik spoke in strong support of Chinuch Atzmai (a bold move since his own Mizrachi party supported the mamlachti dati day schools) and praised Rabbi Kotler as the gadol ha-dor. Rabbi Kotler began tugging at Rabbi Soloveitchik’s sleeve and, with tears running down his face begged him to stop, saying, ‘No, no, dos is nisht emes [that is not true]!’"
p.371-2
[Rav Soloveitchik describing Rav Kotler in his aforementioned speech]
"Something in him speaks, as I would imagine Reb Yoshe Ber Brisker once spoke. Something in him speaks as I would imagine the Chasam Sofer once spoke: indignation, wonderment, anguish and an invoking of one’s responsibility. And [ ] I mean not only the erudition of a gadol m’gedolei ha-dor because to be a gadol–scholarship alone is insufficient. The qualities of a gadol, besides Torah, are warmth, exuberance, tolerance, wonderment: "and warm yourself in the light of talmidei chachamim"–to benefit from their light is not enough. Cold light is worthless; there must be searing light so that one burns himself in its proximity. Reb Aharon, the great Rosh Yeshiva, has no cold light in him; it is hot; it kindles. And as you approach him, you, in turn, become enkindled…I would like to request that the entire audience rise and pay homage."
HaGaon Rav Avrohom Yitzchok HaKohen Kook, Zatzal: The Perspective of the Chazon Ish, Zatzal
“R. Yitzchak Gerstenkorn, the founder of B’nei Brak, told this story: In 5694 (1934), the Rav [i.e., Rav Avraham Yitzchak Kook] was invited to the groundbreaking ceremony of the Beit Yosef (Novardok) Yeshiva in B’nei Brak…At the ceremony, which the Chazon Ish also attended, Rav Kook spoke at length…Throughout the Rav’s address, the large crowd sat quietly in their seats–everyone but the Chazon Ish. He remained standing throughout the speech, listening attentively to every word. He only sat down when the Rav finished speaking and took his own seat."
"R. Tzvi Kagan, who was present at the event, added this revealing piece of information: When the Rav’s address began to draw out, people approached the Chazon Ish and suggested that he sit down. The revered rabbi refused, however, saying, ‘The Torah is standing!’”
from An Angel Among Men, by Simcha Raz, p.375; translated by Rav Moshe D. Lichtman
It’s worth noting that, in his review of this work, Rav Berel Wein stated, "There is so much about Rav Kook that is misunderstood and misportrayed in the Jewish world, that a book that portrays him accurately is invaluable and necessary. This is such a book."
In a letter from the Chazon Ish to Rav Kook that is seen on p. 374 of this work, we see that the Chazon Ish opened by saying, “HaRav HaRoshi HaGaon Rav Avraham Yitzchak HaKohen Kook, Hod K’vod Maran Shlita.” (“The Chief Rabbi, the consummate Torah-scholar, Rav Avraham Yitzchak HaKohen Kook, the glory of the honor of our Master, may he live a long and good life.”)
HaGaon Rav Avrohom Yitzchok HaKohen Kook, Zatzal: The Perspective of HaGaon Rav Shlomo Zalman Auerbach, Zatzal
“Rav Shlomo Zalman, in his earlier years, enjoyed a warm relationship with Rav Avraham Yitzchak [HaKohen] Kook, the first [Ashkenazi] Chief Rabbi of Israel. He would visit with him, observe his actions, and learn from him. Their relationship was so close, in fact, that Rav Kook officiated at Reb Shlomo Zalman’s wedding… Reb Shlomo Zalman’s respect for Rav Kook was evident from the numerous stories he would tell which highlighted the brilliant and charismatic attributes of the Chief Rabbi… Reb Shlomo Zalman never ceased to speak of him with the very highest admiration.”
“Reb Shlomo Zalman’s classic work Me’orei Esh contains approbations from Rav Abba Yaakov Borochov, Rav Isser Zalman Meltzer, and Rav Avraham Yitzchak Kook. The approbation which appears first is that of Rav Kook.”
“Considering Reb Shlomo Zalman’s aversion to matters of a political nature, it was startlingly unusual when he intervened in the internal affairs of a particular organization. Needless to say, the Gaon’s advice was always sought and welcomed, but in the area of organization politics, no one had ever succeeded in eliciting his response in the past. The issue at hand was whether to accept a certain candidate for a key position in this Torah organization. Reb Shlomo Zalman had recommended not to accept the nominee. His unprecedented intervention was triggered by the fact that the candidate in question always referred to Rav Kook as simply ‘Kook.’”
“Once the Gaon was riding in a taxi with one of the rabbanim from Kol Torah. His companion began to relate that he had found the explanation of a complex subject under examination at the yeshiva, in a particular book. But when he mentioned the name of the sefer, Reb Shlomo Zalman stopped him and refused to hear the explanation, saying that the book contained denigrating remarks about Rav Kook.”
from “And From Jerusalem, His Word,” by Rav Hanoch Teller, pp.196-198
There is a fascinating article "How not to make halachic rulings " by Dr Daniel Sperber that is worth while reading. However, there is one particular segment that really came as a surprise to me. In the context of the sheitls made from India he goes into a whole debate whether in fact Hinduism (at least in some versions) is really monotheistic and compatabile/acceptable(?) to Judaism. Read the entire article for some important cavets, but the following extracts should serve as food for though – very interesting indeed: 
