In this talk, we will first introduce several versions of existence and uniqueness theorems for stochastic differential equations(SDEs). Then we will focus on a special type of SDEs, Ito diffusions. We will give a detailed proof of the strong Markov property of Ito diffusions. This talk can be viewed as an extension of math 286 and material is drawn mostly from Chapter 10 of Chung and Williams' $Introduction$ $to$ $Stochastic$ $Integration$.