This review describes computational approaches to the determination of protein structure from sequence. The emphasis is on reduced protein models that are sufficiently accurate to represent protein structure at low resolution, yet are computationally efficient enough to allow the extensive search of phase space required to locate the global minimum from an unfolded state. A discussion of both potential functions and algorithmic simulation strategies for such models are presented, along with a number of specific models that have been developed and successfully applied to proteins as large as myoglobin. The results indicate that significant progress is being made in understanding the requirements for computational prediction of protein structure.