We investigate the algorithmic properties of circuits of bounded treewidth. Here the treewidth of a circuit C is defined as the treewidth of the underlying undirected graph of C, after the vertices corresponding to input gates have been removed. Thus, boolean formulae correspond to circuits of treewidth 1.• Our first main result is an algorithm for counting the number of satisfying assignments of circuits with n input gates, treewidth ω, and at most s · n gates. The running time of our algorithm is 2 n(1−