The idea of conceptual schemes is one of the most influential and widely used notions in contemporary philosophy. Within the analytic tradition the idea occupies a fundamental position in positivist views as well as in replacing them post-positivist conceptions. Outside the analytic tradition a similar idea is of key importance in structuralist and post-structuralist theories. Despite the broad applicability of the notion of a conceptual scheme, its precise sense is far from being evident in the context of various philosophical trends. Moreover, the well-known American philosopher Donald Davidson's position is that any clear, non-metaphorical meaning cannot be as - cribed to that notion at all – the statement which he tried to substantiate in his famous paper On the Very Idea of a Conceptual Scheme published in 1974.The present paper is aimed, firstly, at outlining the historico-philosophical evolution of the idea of conceptual scheme, concentrating on its development in logical positivism and post-positivist theories of such philosophers as Quine, Sellars, Kuhn, et al., and, secondly, at examining Davidson's criticism of both the idea and the position of conceptual relativism which was raised on its ground, revealing the assumptions which that criticism relies on and which concern relations between language and thought, truth and translation, as well as the role of the scheme-content dualism for empiricism and the place of extensionalism in semantics, etc. Our purpose, on the one hand, is to evaluate the historico-philosophical significance of Davidson's criticism; on the other hand, it is to show that his critical arguments remain to be actual since they shed a new light on the idea of conceptual schemes and allow us to determine their place in tackling the fundamental philosophical question of a relation between reality, thought and language.