The sum-product phenomenon has received a great deal of attention, since Erd\"{o}s and Szemer\`{e}di made their well known conjecture that $\max(|A+A|,|AA|) \geq C_{\epsilon} |A|^{2-\epsilon} \forall \epsilon > 0.$ where $A$ is a finite subset of integers and $A+A=\{a+b: a \in A, b \in A \},$ and $AA=\{ab: a \in A, b \in A \}.$ In this talk ,we will discuss the analogy results in finite fields and its applications. In particular, we address how to use Garaev's inequalities to get quantitative sum-product estimates in finite fields and how Fourier analysis could be applied to attack these kinds of problems.