the hawking- penrose singularity theorems tell us that cosmological solutions of einstein's equations generically contain a singularity. but these theorems tell us little about what happens near such a singularity. do the gravitational fields necessarily grow without bound? can causality break down? what about the cosmic censor? work done during the past ten years--both analytical and numerical--has gotten us a lot closer to answers to these questions. we survey this work, discussing both the mathematical ideas and the physical implications. we also discuss the likely direction of future studies.