Atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive owing to the development of accurate and efficient techniques that describe the quantum mechanical behaviour of electrons. Nevertheless, the overwhelming majority of such simulations still assumes that the nuclei behave as classical particles. Historically, this approximation could sometimes be justified owing to the complexity and computational overhead. However, neglecting nuclear quantum effects has become one of the largest sources of error, especially when systems containing light atoms are treated using current state‐of‐the-art descriptions of chemical interactions. Over the past decade, this realization has spurred a series of methodological advances that have dramatically reduced the cost of including these important physical effects in the structure and dynamics of chemical systems. Here, we discuss how these developments are now allowing nuclear quantum effects to become a mainstream feature of molecular simulations. These advances have led to new insights into phenomena that are relevant to different areas of science — from biochemistry to condensed matter — and open the door to many exciting future opportunities