An orientably-regular map is a cellular embedding of a graph or multigraph in an orientable-surface, with the property that the group of orientation- and incidencepreserving automorphisms has a single orbit on the arcs (ordered edges) of the embedding. I will describe a recent computer-assisted determination of all such maps on surfaces of genus 2 to 100, which revealed some interesting patterns, leading to new discoveries about gaps in the genus spectrum of examples that (a) are chiral, and/or (b) have the property that the map or its topological dual has simple underlying graph. The last part is joint work with Jozef Siran and Tom Tucker.