Helly's theorem is a foundational result in geometric combinatorics providing a condition for the non-emptiness of the intersection of a collection of convex sets in Euclidean space. Hadwiger's theorem is a variant of Helly-type theorems involving common transversals to families of convex sets instead of common intersections. In this talk, we discuss these theorems, as well as a quantitative and colorful version of Hadwiger's theorem on the plane.