This chapter covers the main steps of translating psychometric instruments and outlines the ways of securing the equivalence of concepts, items, and tests and questionnaires. It discusses the problem of equivalence in cross-cultural research; examines construct validity and construct equivalence; investigates content validity and content equivalence; and analyzes linguistic equivalence and translation of psychometric instruments. The idea of hypothetical construct has become popular in psychological measurement and test design and lays the theoretical basis of modern psychometrics. The chapter reviews the statistical testing of instruments' measurement invariance. Special attention should be paid to establishing the metric invariance of instruments through multigroup mean and covariance structures(MACS) analyses. It is important to note that the analysis of linguistic equivalence goes hand-in-hand with an examination of the construct and content forms of equivalence. Confirmatory factor analysis and structural equation modeling should be used to establish various kinds of invariance.