The use of surrogate outcomes that predict treatment effect on an unobserved true outcome may have substantial economic and ethical advantages, through reducing the length and size of clinical trials. There has been extensive investigation of the best means of evaluating putative surrogates. We present a systematic review on the evolution of statistical methods for validating surrogates starting from the defining paper of Prentice (1989). We highlight the fundamental differences in the current statistical evaluation approaches, their advantages and disadvantages, and examine the understanding and perceptions of investigators in this area.