I recently finished Невидимые Пустыники Афона, or “invisible desert-dwellers of Athos.”
There is a long-held tradition on Athos that there are 12 (some say 7) ascetics who lead lives of such perfection that they have the gift to appear only to whom they, or God wishes. It is said that the final Divine Liturgy before the Last Judgement will be served by them on the summit of Mount Athos. When one dies, another ascetic is invited to take their place. There is usually a spiritual father, who leads a pure life, who is chosen as the one who administers the Holy Mysteries to these ascetics, however, it has been known that if there is no one available, then they can appear to a lowly Hieromonk for communion (this is the source of many of the stories, they visit a monk, who then tells others of this amazing secret and the ascetics admonish him before leaving to find another confessor.) sometimes they have even appeared to pious pilgrims on the mountain
The book is essentially a collection of anecdotal evidence about their existence. Saint Paisios is the most explicit, saying that he personally knew several of them. It also details the existence of numerous hermits, who, while perhaps not invisible, nevertheless lead extraordinarily severe lives; dedicating themselves to praying for the entire world.
It made me realise how important this is. Non-orthodox might pour scorn on these hermits, but I truly believe that when there are no more monks praying for the world night & day, the end will be very near.