  We investigate loosely bound composite states made of dark matter, where the
binding energy for constituent particles is less than the constituent mass. We
focus on models of nuclear and molecular dark matter, where constituents are
separated by length scales larger than the inverse constituent mass, just like
nuclei and atoms in the Standard Model. The cosmology, structure, and
interactions at underground experiments are described. We find that loosely
bound composites can have a very large cross section for scattering with nuclei
that scales with nucleon number like $\sim A^4$. For some couplings, these
composites produce extremely soft ($\ll$ keV) individual atomic recoils while
depositing a large amount of total recoil energy ($\gg$ keV) in a single
passage through a detector, implying an interesting new class of signatures for
low threshold direct detection.
