ABSTRACT: Investigations of quantum degenerate atomic gases have primarily focused on weakly-interacting systems, well described by mean-field theory. I will discuss experiments that begin to explore the strongly-interacting regime. These and future studies will test the limitations of theoretical techniques developed to treat the many-body problem. One experiment utilizes a Feshbach resonance to produce strong interactions in a dilute Fermi gas. An intermediate-density regime is realized in which the scattering length exceeds the interparticle separation, a condition that also occurs in nuclear and neutron matter. In this regime, the superfluid critical temperature and the interaction energy are both proportional to the Fermi energy with universal proportionality constants that are difficult to calculate but can now be determined experimentally. In a second experiment, strong correlations between bosonic atoms are attained by tightly confining the atoms in an optical lattice potential. For certain lattice geometries, an array of one-dimensional Bose gases can be produced. Application of an additional optical lattice along the one-dimensional Bose gas results in a Mott-insulating transition. In the Mott insulating state, repulsive interactions between the atoms reduce number fluctuations on the individual lattice sites, inhibiting particle mobility and resulting in a loss of phase coherence. This transition is closely related to the conductor-to-insulator transition observed in high-temperature superconducting materials.