  We review ultralong-range Rydberg molecules (ULRM), which are bound states
between a Rydberg atom and one or more ground-state atoms with bond lengths on
the order of thousands of Bohr radii. The binding originates from multiple
electron-atom scattering and leads to exotic oscillatory potential energy
surfaces that reflect the probability density of the Rydberg electron. This
unconventional binding mechanism opens fascinating possibilities to tune
molecular properties via weak external fields, to study spin-resolved
low-energy electron-atom scattering as well as to control and to probe
interatomic forces in few- and many-body systems. Here, we provide an overview
on recent theoretical and experimental progress in the field with an emphasis
on polyatomic ULRMs, field control and spin interactions.
