Optical geometry is a spatial formalism for light propagation in Lorentzian spacetimes. This provides a geometrically interesting and useful framework for gravitational lensing, which is usually treated in terms of the quasi-Euclidean standard approximation instead. In this talk, I will first consider Riemannian optical geometry, and review basic results as well as recent work using the Gauss-Bonnet theorem and curve-shortening flow. In particular, the first isoperimetric inequality in this context will be presented. Then going beyond metric geometry, I will consider possible extensions to Randers-Finsler optical geometry, which arises for stationary spacetimes, and show a connection with the magnetoelectric effect. Finally, a framework for optics in non-metric spacetimes will be discussed.