"Market efficiency" is the basic axiom of Financial Economics and fondamental base for ability of optimal allocation (of financial resources) in a capital market. Vast and extensive studies around Market efficiency in recent decades, has induced strong evolutions in economist’s perception from a Market efficiency, methods of assessing and their implications in real world. This essay attempts to procure a concise leterature review of these evolutions. Results show that applied methods in Iran are incomplete in regard with new addvancements in foreign studies. So, weak form efficiency of Tehran Stock Exchange is reevaluated using new method of H statistic of Hinich. Results of empirical study shows that weak form efficiency is rejected for all the sample as a whole. But, market efficiency would be in evolvotion in studied periods based on used H statistic in this article. Also, market efficiency experienced an stationary improvement  from 2005.