We present a formal method for component-based system specification and verification which is based on the new algebraic specification language CafeOBJ, which is a modern successor of OBJ incorporating several new developments in algebraic specification theory and practice. We first give an overview of the main features of CafeOBJ, including its logical foundations, and then we focus on the behavioural specification paradigm in CafeOBJ, surveying the object-oriented CafeOBJ specification and verification methodology based on behavioural abstraction. The last part of this paper further focuses on a component-based behavioural specification and verification methodology which features high reusability of both specification code and verification proof scores. This methodology constitutes the basis for an industrial strength formal method around CafeOBJ.