Subgraph counting is a fundamental problem in graph analysis that finds use in a wide array of applications. The basic problem is to count or approximate the occurrences of a small subgraph (the pattern) in a large graph (the dataset). Subgraph counting is a computationally challenging problem, and the last few years have seen a rich literature develop around scalable solutions for it. However, these results have thus far appeared as a disconnected set of ideas that are applied separately by different research groups. We observe that there are a few common algorithmic building blocks that most subgraph counting results build on. In this tutorial, we attempt to summarize current methods through distilling these basic algorithmic building blocks. The tutorial will also cover methods for subgraph analysis on “big data” computational models such as the streaming model and models of parallel and distributed computation.