The number of possible unrooted binary trees (phylogenies) increases super-exponentially with the number of taxa. To find the Maximum Likelihood (ML) tree one has to enumerate and evaluate all these trees. As we will see, this is computationally not feasible. Therefore, one predominantly deploys ad hoc tree search methods that strive to find a "good" ML tree in the hope that it will be close, either with respect to the likelihood score or the topological structure, to the globally optimal ML tree. In this chapter we provide an overview over the most popular and efficient ML tree search techniques. How to cite: Alexandros Stamatakis and Alexey M.