Recently I developed a systematic method for determining invariants of families of equations. The method is based on the infinitesimal approach and is applicable to algebraic and differential equations possessing finite or infinite equivalence groups. Moreover, it does not depend on the assumption of linearity of equations. The method was applied to variety of ordinary and partial differential equations. The present paper is aimed at discussing the main principles of the method and its applications with emphasis on the use of infinite Lie groups.