Since its early days in the early 1970, the field of computational rheology (the flow of complex fluids) has experienced a number of insurmountable stumbling blocks, notably, the high Weissenberg number problem (HWNP); it is a term coined to describe the breakdown of computations at a moderately high values of the elasticity parameter. In this lecture I will report a number of recent advances in an effort to elucidate the HWNP, and describe some of the remaining problems.