  We review the field of the glass transition, glassy dynamics and aging from a
statistical mechanics perspective. We give a brief introduction to the subject
and explain the main phenomenology encountered in glassy systems, with a
particular emphasis on spatially heterogeneous dynamics. We review the main
theoretical approaches currently available to account for these glassy
phenomena, including recent developments regarding mean-field theory of liquids
and glasses, novel computational tools, and connections to the jamming
transition. Finally, the physics of aging and off-equilibrium dynamics
exhibited by glassy materials is discussed.
