Compiler verification is essential for the construction of fully verified software, but most prior work (such as CompCert) has focused on verifying whole-program compilers. To support separate compilation and to enable linking of results from different verified compilers, it is important to develop a compositional notion of compiler correctness that is modular (preserved under linking), transitive (supports multi-pass compilation), and flexible (applicable to compilers that use different intermediate languages or employ non-standard program transformations). In this thesis, we formalize such a notion of correctness based on parametric simulations, thus developing a novel approach to compositional compiler verification.