One of the main issues of molecular evolution is to reveal the principles dictating protein evolutionary rates. A traditional hypothesis posits that protein evolutionary rates are mostly determined by the average functional importance of amino acids in a given protein. Thus the correlations of evolutionary rates with different variables such as PPI, gene essentiality and expression abundance have been studied to test the traditional hypothesis. Recently, mRNA expression abundance among the variables has drawn much attention, not only because it shows relatively strong correlation with protein evolutionary rates, but also because of the controversies surrounding an alternative hypothesis against the traditional one. Here, I will give an overview over the traditional hypothesis, and summarize the different variables that have been found to correlate with protein evolutionary rates. Then I will introduce pros and cons on the two different hypotheses.