This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on Recent Advances in Real Complexity and Computation, held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving,...