Given a complex K3 surfaces with a fixed Kahler class, one can construct a family of K3 surfaces over the projective line called the twister space. The theory of twistor spaces is effective for studying the period domain/period map and also leads to the study of hyperholomorphic sheaves, which have peculiar deformation-theoretic properties. Furthermore, similar theories of twistor spaces exist in the context of hyperkahler varieties as well as supersingular K3 surfaces in positive characteristics, which provide further potential applications. In this talk, we plan to stick to the case of complex K3 surfaces and introduce twistor spaces and their basic properties.