Topological properties of real algebraic varieties: du cote de chez Rokhlin

This survey gives an overview of achievements in topology of real algebraic varieties in the direction initiated in the early 1970s by V. I. Arnol'd a nd V. A. Rokhlin. An attempt is made to systematize th principal results in the subject. After an exposition of general tools and results, special att ention is given to surfaces and curves on surfaces.