Future observations are expected to reveal the so-called photon rings in detailed images of black holes. These rings are lensed images of luminous matter surrounding the black hole, formed by photons that loop around it before reaching the observer. In this talk, we present the results of analytical studies of photon rings in the images of spherically symmetric black holes. Specifically, we derive an explicit equation in polar coordinates describing the shape of higher-order photon rings. This formula describes the apparent shape of the higher-order images of the equatorial emission ring with a given radius around the black hole, as seen by a distant observer at an arbitrary inclination. Additionally, we discuss how the black hole metric can be constrained by measuring the relative separation between neighboring photon rings, even without knowing the details of the emission. The talk is mostly based on the papers Bisnovatyi-Kogan, Tsupko (PhysRevD, 2022); Tsupko (PhysRevD, 2022); Aratore, Tsupko, Perlick (PhysRevD, 2024).