abstract: A key open problem within galaxy evolution is to understand the evolution of galaxies towards quiescence. This work investigates the suppression of star-formation through shocks and turbulence at low-redshift, and at higher-redshifts, this work investigates the use of features within quiescent galaxy spectra to redshift estimation, and passive evolution of aging stellar populations to understand their star-formation histories. At low-$z$, this work focuses on the analysis of optical integral field spectroscopy data of a nearby ($z\sim0.0145$) unusual merging system, called the Taffy system because of radio emission that stretches between the two galaxies. This system, although a recent major-merger of gas-rich spirals, exhibits an atypically low star-formation rate and infrared luminosity. Strong evidence of shock heating as a mechanism for these atypical properties is presented. This result (in conjunction with many others) from the nearby Universe provides evidence for shocks and turbulence, perhaps due to mergers, as an effective feedback mechanism for the suppression of star-formation. At intermediate and higher-$z$, this work focuses on the analysis of Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) G800L grism spectroscopy and photometry of galaxies with a discernible 4000\AA\ break. The usefulness of 4000\AA/Balmer breaks as redshift indicators by comparing photometric, grism, and spectrophotometric redshifts (SPZs) to ground-based spectroscopic redshifts, is quantified. A spectral energy distribution (SED) fitting pipeline that is optimized for combined HST grism and photometric data, developed for this project, is presented. This pipeline is a template-fitting based routine which accounts for correlated data between neighboring points within grism spectra via the covariance matrix formalism, and also accounts for galaxy morphology along the dispersion direction. Evidence is provided showing that SPZs typically improve the accuracy of photometric redshifts by $\sim$17--60\%. For future space-based observatories like the Nancy Grace Roman Space Telescope (formerly the Wide Field InfraRed Survey Telescope, i.e., WFIRST) and Euclid, this work predicts $\sim$700--4400 galaxies\,degree$^{-2}$, within $1.6 \lesssim z \lesssim 3.4$, for galaxies with 4000\AA\ breaks and continuum-based redshifts accurate to $\lesssim$2\%. This work also investigates the star-formation histories of massive galaxies ($\mathrm{M_s \geq 10^{10.5}\, M_\odot}$). This is done through the analysis of the strength of the Magnesium absorption feature, Mgb, at $\sim$5175\AA. This analysis is carried out on stacks of HST ACS G800L grism data, stacked for galaxies binned on a color vs stellar mass plane. / Dissertation/Thesis / Doctoral Dissertation Astrophysics and Astronomy 2020