Statistical learning handles uncertainty in a robust and principled way. Relational learning (also known as inductive logic programming (ILP)) models domains involving multiple relations. Recent years have seen a surge of interest in the statistical relational learning (SRL) community in combining the two, driven by the realization that many (if not most) applications require both and by the growing maturity of the two fields.  Markov logic networks (MLNs) is a statistical relational model that has gained traction within the AI community in recent years because of its robustness to noise and its ability to compactly model complex domains. MLNs combine probability and logic by attaching weights to first-order formulas, and viewing these as templates for features of Markov networks.  Learning the structure of an MLN consists of learning both formulas and their weights. To obtain weighted MLN formulas, we could rely on human experts to specify them. However, this approach is error-prone and requires painstaking knowledge engineering. Further, it will not work on domains where there is no human expert.  The ideal solution is to automatically learn MLN structure from data. However, this is a challenging task because of its super-exponential search space. We address this problem by presenting a series of algorithms that efficiently and accurately learn MLN structure.