Tumor growth has been modeled at the macroscopic level by using established physical laws coup
led with biological processes which are described in a phenomenological fashion. Such model c
onsists of a system of PDEs in the tumor region; this region is changing in time, and thus its
boundary is a "free boundary." In this talk, I shall introduce basic material on free bounda
ry problems, and then proceed to describe models of tumor growth. I shall state results on exi
stence theorems, the shape of the free boundary, and on its asymptotic behavior as time goes t
o infinity.