In this thesis, we study the stability of planar rarefaction waves to the Cauchy and the initial boundary value problems for hyperbolic conservation laws. Precisely, we study the following problems: In Chapter 2, we aim to prove the convergence rates of solutions to strong rarefaction waves for two-dimensional viscous conservation law with boundary. In Chapter 3, we study the decay rates of strong planar rarefaction waves to scalar conservation laws with degenerate viscosity. In Chapter 4, we investigate the asymptotic stability of the weak rarefaction wave for Cauchy problem for generalized KdV-Burgers-Kuramoto equation. The analysis is based on a priori estimates and the standard L2-energy method.