Menachem Butler notes that the custom of having portraits done of Rabbinic figures dates back to the 16th century and has now been applied to YU. He also raises the issue of the permissibility of such portraits in like of the injunction against making graven images.
There is a fairly substantial literature on the topic of Rabbinic pictures. In my previous post, I note that Mark included a picture of himself in his book. This was fairly common to include on the frontispiece of ones book a portrait. Menashe ben Israel, Yosef Delemdigo, Yehudah Modena as well as numerous others did so. In Cohen’s book, mentioned by Menachem, he discusses this. R. Reuven Margulies in his Toldot Adam, Lemberg, 1921, 8-9 and Aviad Cohen, De’uknot Hakhamim bein halakha u’masse in Machanayim 2 (1995).
However, the most complete discussion as to the halakhic implications of this custom as well as a fairly extensive list of seforim containing rabbinic frontispices, can be found at the end of book having very little to do with this topic. R. Areyeh Yehuda Leib Lifshitz’s first published in Warsaw in 1927 and reprinted in Israel, 1965. The book is devoted to the somewhat mythical R. Saul Wahl. In the first edition, however, R. Lifshitz included a picture of himself. This picture was placed loose in the book. At the end, R. Lifshitz includes a lengthy teshuva devoted to demonstrating that portraits pose no halakhic problem. [There is also a well know from R. Jacob Emden discussing both a portrait of his father, the Hakam Tzvi as well as a medal struck in honor of the chief rabbi.]
Another, more contemporary article discussing this issue can be found in the book Mo’adim l’Simhah b y R. Tuvia Fraind vol. 1 where he has an article on this.
Perhaps one of the strangest pictures is that of R. Yehuda Aszod. R. Aszod held that it did violate Jewish law to take pictures. His students, however, really wanted a picture of their teacher. They decided on a plan to obtain his picture, that after he was dead to prop him up and take his picture. Sure enough, that is exactly what they did. They also decided that proceeds from the sale of his picture would go to his widow and his children. At his funeral, there was a rather big to do about this especially in light of the fact that it is generally not allowed to profit from the dead. However, some permitted this and his picture was sold. [You can see this picture in the book Gedoli Dorot the three vol. picture/biography book.]
This story is recounted in biography done by his grandson that appears at the beginning of his commentary on the Torah Divrei Maharia. This was first published in 1931 and republished in 1970, in both these editions this story appears, however, in the most recent reprint in 1986 this story has been removed.