  Results on the correlations of low density classical and quantum Coulomb
systems at equilibrium in three dimensions are reviewed. The exponential decay
of particle correlations in the classical Coulomb system -- Debye-H\"uckel
screening -- is compared and contrasted with the quantum case where strong
arguments are presented for the absence of exponential screening. Results and
techniques for detailed calculations that determine the asymptotic decay of
correlations for quantum systems are discussed. Theorems on the existence of
molecules in the Saha regime are reviewed. Finally, new combinatoric formulas
for the coefficients of Mayer expansions are presented and their role in proofs
of results on Debye-H\"uckel screening is discussed.
