This paper provides a comprehensive review of the methods and techniques developed over the past two decades for optimizing continuous gas lift systems. It traces the evolution from isolated single-well analysis to real-time, multivariate optimization approaches that consider the interactions of all wells in an oilfield. While some methods are limited by their failure to account for the interdependencies among well sharing common streamlines, others struggle with scalability and the quality of solutions when applied to large-scale networks of hundreds of wells. The aim of this paper is to offer insights into the development of gas lift optimization methods and highlight the key challenges that remain unresolved in the field.