Ab initio simulations of halide perovskites typically assume that the potential energy felt by electrons is defined with the nuclei fixed at their crystallographic Wyckoff positions. This assumption misses the effect of local disorder (polymorphism) which affects profoundly the mechanical, optoelectronic, and light-absorbing properties of halide perovskites. In this talk, I will discuss the important role of polymorphism and anharmonicity in the electron-phonon coupling of halide perovskites. In particular, I will demonstrate that (i) polymorphism is at the origin of overdamped and strongly coupled vibrational dynamics, (ii) anharmonic optical vibrations dominate thermal renormalization of their band gaps, and (iii) polymorphism is the key to understand the gradual variation of their band gaps around the phase transition temperatures. To address these points we develop a new very efficient methodology for anharmonic lattice dynamics, relying on the special displacement method (A-SDM). The A-SDM is a very simple tool that can be exploited by both condensed matter theorists and experimentalists, opening the way for systematic simulations of anharmonic phonons. Overall, our new theoretical advances set up a new framework for interpreting the fundamental mechanisms driving the optoelectronic, transport, and photovoltaic properties of halide perovskites.