Crystalline polymers are very interesting and useful materials with great versatility through their potential morphology control. Recent surge in computer modeling studies has its origin both in increasing need for efficient methods of materials' design and in tremendous developments in computer power that is expected to meet the need. In this paper, we briefly survey the present state of computer modeling of polymer crystallization with the aim to foresee future developments. We first review Simulations of crystallization in simple polymers under quiescent conditions where most of the efforts have hitherto been devoted. We also examine recent studies on crystallization under flow or large deformation. Then we present our ambitious plans to extend the simulation methods to polymers having complex chemical structures, though it is still an uncultivated field of research. We also refer to the new modeling strategies which integrate macroscopic and microscopic methods, and to the possibilities of molecular modeling in polymer nanotechnologies. Though our goal seems very far, there are obviously very fertile lands for the computer simulation studies. (C) 2009 Elsevier Ltd. All rights reserved.