During this talk we consider various mathematical models of cancer invasion of tissue.

We will focus on two crucial components of tissue invasion, cancer cell proliferation and

the secretion of proteolytic enzymes induced by the cancer cells. The models consist of

reaction-di_usion-taxis partial di_erential equations and, in some cases, it may include

nonlocal kinetic terms. We will present theoretical results for the models as well as

numerical simulations.