I will describe some of the capabilities of SageMath related to topology and homological algebra. From the topological point of view, SageMath can do basic computations with simplicial complexes, simplicial sets, cubical complexes, and semisimplicial sets, including homology and cohomology groups with various coefficients, the cohomology ring with field coefficients, and the fundamental group (modulo the word problem). It can compute mod 2 Steenrod operations on the homology and cohomology of simplicial complexes and simplicial sets. On the algebra side, SageMath has an implementation of the Steenrod algebra, commutative differential graded algebras, and finitely presented graded modules over (for example) the Steenrod algebra. I will provide examples and suggest some directions that SageMath could be expanded and improved.