The objective of this study is mainly to review recent work concerning the numerical modeling of the stick-slip and gross melt fracture polymer extrusion instabilities. Three different mechanisms of instability are discussed: (a) combination of nonlinear slip with compressibility; (b) combination of nonlinear slip with elasticity; and (c) constitutive instabilities. Furthermore, preliminary numerical simulations of the time-dependent, compressible extrudate-swell flow of a Carreau fluid with slip at the wall, using a realistic macroscopic slip equation that is based on experimental data for a high-density polyethylene, are presented.