Recent progress in Lorentz-covariant quantum field theories of the nuclear many-body problem (quantum hadrodynamics, or QHD) is discussed. The effective field theory studied here contains nucleons, pions, isoscalar scalar (&sigma) and vector (&omega) fields, and isovector vector (&rho) fields. The theory exhibits a nonlinear realization of spontaneously broken SU(2)LxSU(2)R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the nuclear currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying theory of quantum chromodynamics, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. Moreover, it has recently been verified that for normal nuclear systems, it is possible to systematically expand the effective Lagrangian in powers of the meson fields (and their derivatives) and to truncate the expansion reliably after the first few orders. Using a mean-field version of the energy functional, accurate quantitative results are obtained for the bulk and single-particle properties of medium- and heavy-mass nuclei. The importance of modern perspectives in effective field theory and density functional theory for understanding these successes of QHD is emphasized.