Cobordisms are a useful organizing principle for a wide range of problems in manifold topology. In dimensions 5 or higher, theorems about corbordisms are some of the most important and generally powerful tools we have, and significant study has been devoted to cobordism problems in these high dimensions. While cobordism theory has been historically less important in low dimensions, massive recent progress in 3—manifold theory has been made through the use of modern homology theories (like Heegaard Floer and Khovanov Homology) which interact very well with cobordisms. These new theories have opened the doors to a world of interesting new cobordism problems, where we can ask questions directly about the combinatorics of building manifolds and work with representation theory-style algebra.