The remarkable Hubble Space Telescope (HST) data sets from the CANDELS, HUDF09, HUDF12, ERS, and BoRG/HIPPIES programs have allowed us to map the evolution of the rest-frame UV luminosity function (LF) from to . We develop new color criteria that more optimally utilize the full wavelength coverage from the optical, near-IR, and mid-IR observations over our search fields, while simultaneously minimizing the incompleteness and eliminating redshift gaps. We have identified 5859, 3001, 857, 481, 217, and 6 galaxy candidates at , , , , , and , respectively, from the ∼1000 arcmin2 area covered by these data sets. This sample of >10,000 galaxy candidates at is by far the largest assembled to date with HST. The selection of 4–8 candidates over the five CANDELS fields allows us to assess the cosmic variance; the largest variations are at . Our new LF determinations at and span a 6 mag baseline and reach to –16 AB mag. These determinations agree well with previous estimates, but the larger samples and volumes probed here result in a more reliable sampling of galaxies and allow us to reassess the form of the UV LFs. Our new LF results strengthen our earlier findings to significance for a steeper faint-end slope of the UV LF at , with α evolving from at to at (and at ), consistent with that expected from the evolution of the halo mass function. We find less evolution in the characteristic magnitude M* from to the observed evolution in the LF is now largely represented by changes in . No evidence for a non-Schechter-like form to the z ∼ 4–8 LFs is found. A simple conditional LF model based on halo growth and evolution in the M/L ratio of halos provides a good representation of the observed evolution.