abstract: Matroid theory is a structurally rich branch of combinatorics with pervasive connections with geometry, topology, and algebra. In this expository talk I will gently introduce the notion of matroid and illustrate some of applications. Then — with an view towards topological applications — I will go on to more refined combinatorial structures such as oriented matroids. I will conclude with a recent and already thriving new character among matroidal theories: Baker's matroids over hyperfields. Time permitting, I will also outline some of the main open research directions revolving around these objects.