Consider $n\times n$ Hermitian random matrices $M_n$ with i.i.d entries with mean zero, variance one and bounded high moments. I will discuss the recent progresses in studying the eigenvalue statistics at small scales, especially the local semi-circle law. In joint work with Van Vu, we are able to prove the local semi-circle law for $\frac{1} {\sqrt{n}} M_n$ on the scale of $\log n/ n$. As a consequence, we can show that any unit eigenvector, whose eigenvalue is bounded away from the spectral edges, is delocalized in the sense that the infinity norm has upper bound $\sqrt{\log n/n}$.