  The class `bulges' contains objects with very different formation and
evolution paths and very different properties. I review two types of `bulges',
the boxy/peanut bulges (B/Ps) and the discy bulges. The former are parts of
bars seen edge-on, have their origin in vertical instabilities of the disc and
are somewhat shorter in extent than bars. Their stellar population is similar
to that of the inner part of the disc from which they formed. Discy bulges have
a disc-like outline, i.e., seen face-on they are circular or oval and seen
edge-on they are thin. Their extent is of the order of 5 times smaller than
that of the boxy/peanut bulges. They form from the inflow of mainly gaseous
material to the centre of the galaxy and from subsequent star formation. They
thus contain a lot of young stars and gas. Bulges of different types often
coexist in the same galaxy. I review the main known results on these two types
of bulges and present new simulation results. B/Ps form about 1Gyr after the
bar, via a vertical buckling. At that time the bar strength decreases, its
inner part becomes thicker -- forming the peanut or boxy shape -- and the ratio
$\sigma_z^2/\sigma_r^2$ increases. A second buckling episode is seen in
simulations with strong bars, also accompanied by a thickening of the peanut
and a weakening of the bar. The properties of the B/Ps correlate strongly with
those of the bar: stronger bars have stronger peanuts, a more flat-topped
vertical density distribution and have experienced more bucklings. I also
present simulations of disc galaxy formation, which include the formation of a
discy bulge. Decomposition of their radial density profile into an exponential
disc and a Sersic bulge gives realistic values for the disc and bulge
scale-lengths and mass ratios, and a Sersic shape index of the order of 1.

Astrophysics