Father Zuhlsdorf has issued the call for prayer, and I am adding my two cents' worth.
There are two noteworthy efforts the Church is making toward unity, either would be a great step forward.
On the one hand are the ongoing efforts to restore the unity that once existed between Catholic and Orthodox. This is a thorny subject, usually misunderstood; but the long and short of it is that East and West are very close to each other in what we believe, and yet because of a lot of history, and some fundamental differences, less in Faith per se, but in structure and culture, create excessive complications in restoring unity.
For one thing, because the various Orthodox Churches do not have their own pope, as it were--they do not have the same structure amongst themselves that the Church of the West has--it makes it very hard for "the Orthodox" to respond. Bishops and theologians can respond, tentatively, but the goal is not simply communion with this or that Orthodox theologian or prelate, but between sister Churches. If segments of Orthodoxy restore communion with Rome, while others don't, that only replicates what happened in centuries past, and creates new barriers to overcome.
At any rate, there are always hints and hopes. As has become common, the Patriarch of Constantinople (aka Istanbul), the preeminent Orthodox prelate, will join the Patriarch of Rome (yes, I know the pope doesn't use the title anymore, but that's still who he is) this Sunday for the Solemnity of Peter and Paul. You may recall the Holy Father journeyed to Istanbul last year and prayed with Bartholemew on a feast of importance to the East, but I have forgotten which it was, Saint Andrew I believe?
And then there is a wound in the unity of the Roman Church, involving those who especially identify with Catholic Tradition and the ancient liturgy. I mean the Society of Saint Pius X.
This is the group that is identified with the late Archbishop Lefebvre; and some may recall that when he ordained four bishops in 1988 without clear approbation of our late Holy Father, John Paul of happy memory, this created a wound that continues to this day.
Pope Benedict has made many efforts toward reconciliation, most prominent--but hardly the only one--was his move to make the older form of the Mass freely available, and to restore it as a vital part of our lived tradition. Recently, the pope--or someone acting for him--communicated to the current superior of the SSPX some expectations of mutual charity as a basis for further work together. Some are calling them "demands"--but when you see what was requested, it seems so elementary:
1. A commitment to a proportioned response to the generosity of the Pope.
2. A commitment to avoid any public speech which does not respect the person of the Holy Father and which can be negative for ecclesial charity.
3. A commitment to avoid the pretense of a Magisterium superior to the Holy Father and to not put forward the Fraternity [SSPX] in opposition to the Church.
4. A commitment to demonstrate the will to behave honestly in full ecclesial charity and in respect to the authority of the Vicar of Christ.
5. A commitment to respect the date – fixed at the end of the month of June – to respond positively. This will be a required and necessary condition for the immediate preparation for adhesion to have full communion.
Please note what was not specified--nothing about celebrating the newer form of the Mass or sacraments, nothing about Vatican II, nothing about any doctrinal questions whatsoever. Some will say, but aren't those important? Yes, of course they are, and they must be addressed in some fashion. But what is noteworthy is that the Holy Father is asking such basic things as a starting point.
(I might add that this gives us all a reminder for each of us--may everyone of us always "avoid any public speech which does not respect the person of the Holy Father and which can be negative for ecclesial charity" and not assume a "pretense of a Magisterium superior" to that of the Church.)
Father Z rightly observes that this may be a key moment, so pray, pray pray!