Computer studies of complex physical phenomena, especially those utilizing MD (molecular dynamics) simulation, are often resource intensive. Supercomputer architecture, now mainly based on highly parallel GPUs (graphics processing units), is becoming increasingly complicated, so that designing efficient algorithms is a far more difficult task than it once was. Following a brief historical introduction, GPU architecture will be outlined, and novel GPU algorithms surveyed. MD methods will then be reviewed, and some of the unique demands they impose on the GPU described and resolved, with emphasis on the performance gains. The talk concludes with a discussion of several MD studies of emergent phenomena. Lessons learned while adapting MD for the GPU should be valuable in other contexts where compatibility between algorithms and hardware may not be apparent.