Unsurprisingly, the random graph is a graph that has been constructed in a random manner. However, the exact nature of this construction is of interest as it has been shown that many real-world networks share the structural properties of particular sorts of randomly constructed networks. We will focus on the two most common approaches, Erdős-Rényi and Barabási-Albert models, and show some well known emergent patterns of these approaches. We will also refresh some of the graph-related notions that will be discussed in the following talk.