We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) data and a recent reanalysis of Type Ia supernova (SN) data. In particular, we take advantage of high-precision BAO measurements from galaxy clustering and the Lyman-$\ensuremath{\alpha}$ forest (LyaF) in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). Treating the BAO scale as an uncalibrated standard ruler, BAO data alone yield a high confidence detection of dark energy; in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Adding the CMB-calibrated physical scale of the sound horizon, the combination of BAO and SN data into an ``inverse distance ladder'' yields a measurement of ${H}_{0}=67.3\ifmmode\pm\else\textpm\fi{}1.1\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, with 1.7% precision. This measurement assumes standard prerecombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology is an important corroboration of this minimal cosmological model. For constant dark energy ($\mathrm{\ensuremath{\Lambda}}$), our $\mathrm{BAO}+\mathrm{SN}+\mathrm{CMB}$ combination yields matter density ${\mathrm{\ensuremath{\Omega}}}_{m}=0.301\ifmmode\pm\else\textpm\fi{}0.008$ and curvature ${\mathrm{\ensuremath{\Omega}}}_{k}=\ensuremath{-}0.003\ifmmode\pm\else\textpm\fi{}0.003$. When we allow more general forms of evolving dark energy, the $\mathrm{BAO}+\mathrm{SN}+\mathrm{CMB}$ parameter constraints are always consistent with flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ values at $\ensuremath{\approx}1\ensuremath{\sigma}$. While the overall ${\ensuremath{\chi}}^{2}$ of model fits is satisfactory, the LyaF BAO measurements are in moderate ($2--2.5\ensuremath{\sigma}$) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshift remain consistent with our expansion history constraints, and they yield a higher ${H}_{0}$ and lower matter clustering amplitude, improving agreement with some low redshift observations. Expansion history alone yields an upper limit on the summed mass of neutrino species, $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.56\text{ }\text{ }\mathrm{eV}$ (95% confidence), improving to $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.25\text{ }\text{ }\mathrm{eV}$ if we include the lensing signal in the Planck CMB power spectrum. In a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model that allows extra relativistic species, our data combination yields ${N}_{\mathrm{eff}}=3.43\ifmmode\pm\else\textpm\fi{}0.26$; while the LyaF BAO data prefer higher ${N}_{\mathrm{eff}}$ when excluding galaxy BAO, the galaxy BAO alone favor ${N}_{\mathrm{eff}}\ensuremath{\approx}3$. When structure growth is extrapolated forward from the CMB to low redshift, standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates.