While the major contribution to the cosmic microwave background (CMB) aniso
tropies are the sought-after primordial fluctuations produced at the surfac
e of last scattering, other effects produce secondary fluctuations at lower
redshifts. Here we study the extragalactic foregrounds of the CMB in the c
ontext of the upcoming Microwave Anisotropy Probe (MAP) mission. We first s
urvey the major extragalactic foregrounds and show that discrete sources, t
he Sunyaev-Zeldovich (SZ) effect, and gravitational lensing are the most do
minant ones for MAP. We then show that MAP is expected to detect (> 5 sigma
) about 46 discrete sources directly with 94 GHz fluxes above 2 Jy. The mos
t prominent SZ features on the CMB sky are rich clusters of galaxies. In pa
rticular, we show that the Coma Cluster will be clearly detected and margin
ally resolved by MAP. We then consider a cosmological population of cluster
s, and show that MAP should detect (> 5 sigma) about 10 SZ clusters directl
y. The mean SZ fluxes of fainter clusters can be probed by cross-correlatin
g MAP with cluster positions extracted from existing catalogs. For instance
? a MAP-XBACs cross-correlation will be sensitive to clusters with S(94 GHz
)greater than or similar to 200 mJy, and will thus provide a test of their
virialization state and a measurement of their gas fraction. Finally, we co
nsider probing the hot gas on supercluster scales by cross-correlating the
CMB with galaxy catalogs. Assuming that galaxies trace the gas, we show tha
t a cross-correlation between the (MAP) and the Automatic Plate Measuring F
acility (APM) catalog should yield a marginal detection, or at least a four
fold improvement on the COPE upper limits for the rms Compton y parameter.