The importance of protein folding has been recognised for many years. Almost a half century ago, Linus Pauling discovered two quite simple, regular arrangements of amino acids--the alpha-helix and the beta-sheet that are found in almost every protein. In the early 1960s, Christian Anfinsen showed that the proteins actually "tie" themselves: If proteins become unfolded, they fold back into proper shape of their own accord; no shaper or folder is needed. The nature of the unfolded state plays a great role in understanding proteins. Alzheimer's disease, cystic fibrosis, mad cow disease, and many cancers are inherited emphysema. Recent discoveries show that all these apparently unrelated diseases result from protein folding gone wrong. Theoretical and computational studies have recently achieved noticeable success in reproducing various features of the folding mechanism of several small to medium-sized fast-folding proteins. This survey presents the state-of-the-art in protein structure prediction methods from a computer scientist perspective.