  We explore observational and theoretical constraints on how galaxies might
transition between the "star-forming main sequence" (SFMS) and varying "degrees
of quiescence" out to $z=3$. Our analysis is focused on galaxies with stellar
mass $M_*>10^{10}M_{\odot}$, and is enabled by GAMA and CANDELS observations, a
semi-analytic model (SAM) of galaxy formation, and a cosmological
hydrodynamical "zoom in" simulation with momentum-driven AGN feedback. In both
the observations and the SAM, transition galaxies tend to have intermediate
S\'ersic indices, half-light radii, and surface stellar mass densities compared
to star-forming and quiescent galaxies out to $z=3$. We place an observational
upper limit on the average population transition timescale as a function of
redshift, finding that the average high-redshift galaxy is on a "fast track"
for quenching whereas the average low-redshift galaxy is on a "slow track" for
quenching. We qualitatively identify four physical origin scenarios for
transition galaxies in the SAM: oscillations on the SFMS, slow quenching, fast
quenching, and rejuvenation. Quenching timescales in both the SAM and the
hydrodynamical simulation are not fast enough to reproduce the quiescent
population that we observe at $z\sim3$. In the SAM, we do not find a clear-cut
morphological dependence of quenching timescales, but we do predict that the
mean stellar ages, cold gas fractions, SMBH masses, and halo masses of
transition galaxies tend to be intermediate relative to those of star-forming
and quiescent galaxies at $z<3$.
