A fundamental idea in topology is that of a bundle, which can loosely be defined as a continuous family of copies of a space F, parameterized by points in another space B. This idea can be adapted to combinatorics in several contexts. A combinatorial bundle should be a "combinatorially continuous" family of combinatorial objects, where the notion of continuity is chosen to both illuminate the combinatorics and tie the combinatorics to topological bundle theory. I will discuss two such combinatorial theories. The first, matroid bundles, models real vector bundles by placing oriented matroids in the role of real vector spaces. The close connections between matroid bundles and real vector bundles have led both to combinatorial results on differential manifolds and topological results on posets of oriented matroids. Another line of work models piecewise-linear (PL) bundles by considering "continuous families" of combinatorial types of cell complexes, where continuity is defined in terms of subdivision. Among the interesting special cases is a model for PL sphere bundles in terms of combinatorial types of convex polytopes and regular subdivision maps between them. This theory leads to an elegant combinatorial presentation of the classifyingspaces BPL(M) and a new categorical perspective on the combinatorics of subdivision.