The last decade has witnessed an explosion of research investigating the role of topology in band-structure, as exemplified by the wealth of recent works on topological insulators and semimetals. In this talk I hope to convince you that low-energy terahertz probes of solids give unique insight into these topological states of matter. First, I will discuss how we can probe the special low-energy electrodynamics of three-dimensional topological insulators using time-domain terahertz spectroscopy. I will then discuss our work following the evolution of the response as a function of magnetic field from a semi-classical transport regime to a quantum regime. In the latter case, we find evidence for Faraday and Kerr rotation angles quantized in units of the fine structure constant. This is consistent with the long-sought “axion electrodynamics” and the topological magneto-electric effect of three-dimensional topological insulators. Among other aspects this gives a purely solid-state measure of the fine structure constant based on a topological invariant. Finally, I will present our most recent studies on measuring emitted terahertz pulses from topological semimetals to identify the intrinsic topological photocurrent.