  We use broadband photometry extending from the rest-frame UV to the near-IR
to fit the individual spectral energy distributions (SEDs) of 63 bright
(L(Ly-alpha) > 10^43 ergs/s) Ly-alpha emitting galaxies (LAEs) in the redshift
range 1.9 < z < 3.6. We find that these LAEs are quite heterogeneous, with
stellar masses that span over three orders of magnitude, from 7.5 < log M <
10.5. Moreover, although most LAEs have small amounts of extinction, some
high-mass objects have stellar reddenings as large as E(B-V) ~0.4.
Interestingly, in dusty objects the optical depths for Ly-alpha and the UV
continuum are always similar, indicating that Ly-alpha photons are not
undergoing many scatters before escaping their galaxy. In contrast, the ratio
of optical depths in low-reddening systems can vary widely, illustrating the
diverse nature of the systems. Finally, we show that in the star formation rate
(SFR)-log mass diagram, our LAEs fall above the "main-sequence" defined by z ~
3 continuum selected star-forming galaxies. In this respect, they are similar
to sub-mm-selected galaxies, although most LAEs have much lower mass.
