Understanding discrete structures of data has been an important and ongoing effort in the communities of machine learning, optimization and statistics. We will introduce the problem under a wide range of generative models, including the well-known Stochastic Block Model and Gaussian Mixture Model. After discussing several popular algorithms, we will present an algorithm based on semidefinite programming (SDP) relaxation. We show that despite being a relaxation, this algorithm achieves an optimal (or 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, a property many algorithms lack.