A certain illustrious scholar once visited the Alter Rebbe (Rabbi Shneur Zalman, founder of Chabad Chasidut) and asked that he turn him into a chasid. "That I cannot do," replied the Alter Rebbe, "the frozen seas will be warmed up by Moshiach."
(L'Chaim)

The occupation of the entire world will be solely to know G-d (Maimonides). A businessman is involved in his occupation all day long. Even his times of rest and sleep are devoted to regaining energy that will enable him to redouble his involvement in his occupation. Even when he sleeps he dreams about his business. This is how Torah will be studied in the time to come.(The Rebbe, 5745-1984)
(L'Chaim)

A gentile landlord once asked a chasid: "What will you do if your Moshiach comes and I won't believe in him?" Replied the chasid: "If you won't believe in him, I won't believe in him either!"
(L'Chaim)

At the time of the supreme revelation of the Divine Presence, all of humanity -- even persons so unspiritual as to be described as "flesh" -- will attain a level of perceptiveness that will inspire them to bow down humbly before their Maker.(Likutei Torah of Rabbi Shneur Zalman)
(L'Chaim)

"Moshiach will come in order to cause the righteous to return in repentance."(Zohar III, 153b)

When Moshiach comes, such a sublime level of Divinity will be revealed that ... even a tzadik [a completely righteous person] will be aroused with feelings of teshuva (repentance). We are not speaking of teshuva of the ordinary kind: this is not relevant to a tzadik, for he has had no taste of sin.(Likutei Torah of Rabbi Shneur Zalman)
(L'Chaim)

When the Jewish people hear the shofar, they are capable of bringing about the final Redemption. When they sound their shofars in fulfillment of the mitzva of Rosh Hashana, their hearts are opened, they shudder over their sins, and in a brief moment their reflections turn to repentance. They barely conclude their shofar blast and the sound of the shofar of Moshiach is already heard. The shofar sounds blend -- his and theirs -- and behold, Redemption comes.(From Book of Our Heritage by Rabbi E. Kitov)
(L'Chaim)

If Moshiach should appear during the days between Rosh Hashana and Yom Kippur, it is conceivable that we will eat and drink on Yom Kippur if it falls during the seven-day dedication of the Third Holy Temple. This was the case with the First Temple, whose dedication began on the eighth of Tishrei, and the people of that time ate and drank on Yom Kippur.(Sefer HaSichot of the Rebbe, 5749)
(L'Chaim)

Sukkot is referred to as Chag HaAssif -- the harvest festival. This name also relates to the Jews' gathering together with Ahavat Yisrael [love for one's fellow Jew]. Such gatherings precipitate the ultimate gathering of the Jewish people which will take place at the time of the Redemption. For when division and strife, the cause of the exile, are nullified, the exile itself, the effect, will be nullified.(The Rebbe, Sukkot 5752-1992)
(L'Chaim)

R. Yitzchak Aizik of Homil, a chasid of scholarly renown, once said: "When Moshiach comes and the dead will be resurrected, among them will rise the Patriarchs, the leaders of the Twelve Tribes, Moshe and Aharon, all the prophets, all the tannaim and amoraim, and the geonim [great Torah sages] and tzadikim of all the generations. And whom will they seek out to rejoice with? The simple Jews."
(L'Chaim)

In the days of Moshiach, the body too will change. It will be like the body of Adam before the sin of the Tree of Knowledge, clear of any evil. As the Midrash states, "His heel threw a shadow on the orb of the sun." That is to say, his body was nullified to the Divine Will even more than was the inanimate sun.(Derech Chaim)
(L'Chaim)

In time to come, Divinity will be revealed in this world at a level more sublime than the level at which it is revealed in the Higher Garden of Eden. This is why even the loftiest tzadikim [righteous people] such as Avraham and Moshe, whose abode is at the zenith of the Higher Garden of Eden, will become vested in corporeal bodies and will arise at the Resurrection of the Dead.(Likutei Torah)
(L'Chaim)

About the coming of Moshiach, Rabbi Shneur Zalman (the first Rebbe of Chabad) said that it will be written in the newspapers. That is just an expression. The actual meaning is that every single Jew will be ready for the coming of Moshiach exactly as if it were written in the newspaper that Moshiach is already on the way!(Torat Sholom of the Rebbe Rashab)
(L'CHAIM)

In the time to come it will be apparent in every entity that it is the handiwork of G-d's creation. People will be able to perceive how the true nucleus of each particular entity, with its distinctive features and characteristics, is the Word of G-d -- that is -- the particular Divine Utterance which suffuses it with vitality and grants it life.(Likutei Sichot, 29)
(L'Chaim)

Rav said, "The world was created only for [King] David." Shmuel said, "The world was created only for Moshe." Rabbi Yochanan said, "The world was created only for Moshiach."(Talmud Sanhedrin 88b)
(L'Chaim)

Presiding over the trial on the "Day of Judgement" will be Moshiach himself... He will weigh and consider the bleak life that Jews have lived in exile. He will intercede on their behalf and seek out their merits, pointing out that they did not want to sin: they were unable to overcome their Evil Inclination. Moshiach will see everyone's virtues.(Likutei Diburim of Rabbi Yosef Yitzchak Schneersohn)
(L'Chaim)

In these times, when the approaching footsteps of Moshiach are close upon us, the principle service of G-d is the service of charity, as our Sages taught, "Israel will be redeemed only by virtue of charity." ...The way to cleave to the Divine Presence in our times is through the practice of charity.(Rabbi Shneur Zalman, based on Tanya-Iggeret HaKodesh)
(L'Chaim)

As is widely known, in future times, Jewish law will follow the view of the school of Shammai. The question thus arises: If Moshiach arrives on the eve of Chanuka, will this reversal in legal rulings take effect immediately, so that on the first evening of the festival we will kindle eight lights?(The Rebbe, on the eve of Chanuka, 5750-1989)
(L'Chaim)

May G-d grant that every one of us should take along the teachings of the Chanuka candles into each and all the days ahead, from this Chanuka to the next, and this will hasten the true and complete Redemption, when G-d "will put an end to the darkness" of this Exile and send us our true Redeemer, Moshiach Tzidkeinu.(The Rebbe, 7th day of Chanuka, 5738)
(L'Chaim)

Whoever does not believe in the involvement of Divine Providence in every aspect of this world, is enslaved to that which covers and conceals Divine Providence. In the future, however, when the spirit of impurity will be removed from the earth, this Providence will become manifest; at that time, everyone will see how every single occurrence derives from G-d.(Kesser Shem Tov)
(L'Chaim)

Elijah the Prophet refined his body to the extent that when he left this world, even his body ascended in the stormwind heavenwards. This is why Elijah specifically is the prophet connected with the tidings of the Redemption -- for in the future even man's flesh will be refined, to the point that "Together all flesh shall see that the mouth of G-d has spoken."(Likutei Sichot, vol. 2)
(L'Chaim)