This talk addresses a coupled chemotaxis-haptotaxis system modeling cancer cell invasion of surrounding tissue,which describes the interactions between the cancer cell density,the concentration of a matrix-degrading enzyme(MDE)and the density of extracellular matrix(ECM).In addition to random movement,cancer cells are supposed to bias their movement both towards increasing concentrations of urokinase plasminogen activator by chemotaxis,and towards increasing densities of the non-diffusible ECM through detecting the macromolecules adhered therein by haptotaxis.It is assumed that the cancer cells undergo birth and death in a logistic manner,competing for space with the ECM.The MDE is assumed to be produced by cancer cells,and to diffuse and decay,whereas the ECM is assumed to be degraded upon contact with MDE.We first discuss the global existence and boundedness of the solutions to the system for appropriate parameter conditions.Then we consider the dominance of chemotaxis whenever the initial ECM density is "small" in certain sense.We next study the asymptotic behavior of solutions when the initial cell density has a positive lower bound in addition to some smallness assumption on initial ECM density.Finally,we briefly review some related results for haptotaxis-only system and for coupled chemotaxis-haptotaxis system.This talk is based on a coupl of joint works with Prof.Michael Winkler at University of Paderborn.