We develop an iterated homology theory for simplicial complexes. This theory is a variation on one due to Kalai. For \Delta a simplicial complex of dimension d-1, and each r=0,...,d, we define rth iterated homology groups of \Delta. When r=0, this corresponds to ordinary homology. If \Delta is a cone over \Delta', then when r=1, we get the homology of \Delta'. If a simplicial complex is (nonpure) shellable, then its iterated Betti numbers give the restriction numbers, h_{k,j}, of the shelling. Iterated Betti numbers are preserved by algebraic shifting, and may be interpreted combinatorially in terms of the algebraically shifted complex in several ways. In addition, the depth of a simplicial complex can be characterized in terms of its iterated Betti numbers.