Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.