  We construct a variety of new exactly-solvable quantum systems, the
potentials of which are given in terms of Lambert-W functions. In particular,
we generate Schr\"odinger models with energy-dependent potentials, conventional
Schr\"odinger models using the supersymmetry formalism, and two-dimensional
Dirac systems. In addition, we derive Wronskian integral formulas for Lambert-W
functions.
