Let $H^2$ denote the Hardy space on the open unit disk $\mathbb{D}$. For a given holomorphic self map $\varphi$ of $\mathbb{D}$, the composition operator $C_{\varphi}$ on $H^2$ is defined by $C_{\varphi} (f)=f\circ \varphi.$ In this talk, we discuss about Beurling type invariant subspace of composition operators, that is common invariant subspaces of shift and composition operators and model spaces invariant under composition operators. The role of Blaschke products for this study will be explained in detail.