An undirected graph is connected if there is a path between any pair of its vertices. In a digraph, connectivity implies there is a path between any two of its vertices in both directions. We start this chapter by defining the parameters of vertex and edge connectivity. We continue by describing algorithms to find cut-vertices and bridges of undirected graphs. We then review algorithms to find blocks of graphs and strongly connected components of digraphs. We describe the relationship between connectivity, and network flows and matching and review sequential, parallel and distributed algorithms for all of the mentioned topics.