Fractal uncertainty principles quantify the extent to which a function and its Fourier transform can be simultaneously localized near a fractal set. They were first introduced and employed by Dyatlov and Zahl in their study of spectral gaps and are related to various topics in quantum chaos and harmonic analysis. In this talk, we will discuss the formulation of such principles for discrete Cantor-like sets known as ellipsephic sets and present some recent work in this area.