Much of the focus of exoplanet atmosphere analysis in the coming decade will be atinfrared wavelengths, with the planned launches of the James Webb Space Telescope (JWST) and the Wide-Field Infrared Survey Telescope (WFIRST). However, without being placed in the context of broader wavelength coverage, especially in the optical and ultraviolet, infrared observations produce an incomplete picture of exoplanet atmospheres. Scattering information encoded in blue optical and near-UV observations can help determine whether muted spectral features observed in the infrared are due to a hazy/cloudy atmosphere, or a clear atmosphere with a higher mean molecular weight. UV observations can identify atmospheric escape and mass loss from exoplanet atmospheres, providing a greater understanding of the atmospheric evolution of exoplanets, along with composition information from above the cloud deck. In this white paper we focus on the science case for exoplanet observations in the near-UV; an accompanying white paper led by Eric Lopez will focus on the science case in the far-UV.