Remez-type inequalities play an important role in approximation theory. This topic was initiated in the work of Remez in 1936, in which he found a sharp constant in an inequality of this type for algebraic polynomials. At the end of the 20th century, a new surge of works on this topic was observed. The efforts of many mathematicians aimed at finding the sharp constant in the Remez-type inequality for trigonometric polynomials. Only in 2019 this problem was solved in the work of Tikhonov and Yuditski. In the author’s works, Remez-type inequalities were extended to wider classes of functions. In this chapter, sharp Remez-type inequalities for functions with a given comparison function are obtained in various metrics. As a result, such type of inequalities were proved for functions from the Sobolev classes, for trigonometric polynomials and polynomial splines with a given ratio of norms of their positive and negative parts.