We will introduce the clustering problem under Gaussian Mixture Model. After discussing several popular algorithms, we will present an algorithm based on semidefinite programming (SDP). We show that despite being a relaxation, this algorithm achieves a nearly optimal error rate in terms of distance to the target solution, and that this result is enabled by a surprising connection with an Oracle integer program. Moreover, this algorithm is robust under the so-called semirandom model, for which understanding of many algorithms is lacking. Time permitting, we will discuss the optimality and robustness of SDP for the clustering problem under a closely related network model.