  The protein folding problem has attracted an increasing attention from
physicists. The problem has a flavor of statistical mechanics, but possesses
the most common feature of most biological problems -- the profound effects of
evolution. I will give an introduction to the problem, and then focus on some
recent work concerning the so-called ``designability principle''. The
designability of a structure is measured by the number of sequences that have
that structure as their unique ground state. Structures differ drastically in
terms of their designability; highly designable structures emerge with a number
of associated sequences much larger than the average. These highly designable
structures 1) possess ``proteinlike'' secondary structures and motifs, 2) are
thermodynamically more stable, and 3) fold faster than other structures. These
results suggest that protein structures are selected in nature because they are
readily designed and stable against mutations, and that such selection
simultaneously leads to thermodynamic stability and foldability. According to
this picture, a key to the protein folding problem is to understand the
emergence and the properties of the highly designable structures.
