  Ultracold molecules confined in optical lattices or tweezer traps can be used
to process quantum information and simulate the behaviour of many-body quantum
systems. Molecules offer several advantages for these applications. They have a
large set of stable states with strong transitions between them and long
coherence times. They can be prepared in a chosen state with high fidelity, and
the state populations can be measured efficiently. They have controllable
long-range dipole-dipole interactions that can be used to entangle pairs of
molecules and generate interesting many-body states. We review the advances
that have been made and the challenges still to overcome, and describe the new
ideas that will unlock the full potential of the field.
