The classical evolutionary game theory, pioneered by Maynard Smith and Price (1973), was initially developed in the context of uni-population games with discrete strategy space. Recently some progress has been made in extending the original idea of Maynard Smith and his collaborators into uni-population games with continuous strategy space (Apaloo, 1997; Christiansen, 1991; Cressman, 2006; Eshel, 1983). The current paper reviews them in a unifying framework, and provides some new theorems linking various concepts of evolutionary stability proposed by different authors.