Excited states of atoms and molecules exhibit a rich array of diverse phenomena. This dissertation examines two exotic states of atoms at such excited levels: Rydberg molecules and atomic negative ions. Rydberg molecules are formed by a Rydberg atom and one or more ground state atoms, and can be highly polar due to their unusual electronic wave functions and enormous bond lengths. This dissertation expands the theory of these molecules by studying the formation and structure of polyatomic molecules, multichannel Rydberg molecules formed from divalent atoms, and spin effects and relativistic interactions. It also details intermolecular forces between Rydberg molecules, their manipulation via external fields, and their dependence on the intricacies of electron-atom scattering. This electron-atom interaction is also the main component of the latter portion of this thesis, which studies doubly excited states of alkali negative ions in very polarizable and nearly degenerate atomic states. Photodetachment of these states reveals electron correlation and long-range forces stemming from their high excitation.