The atoms in conventional (i.e. alkai) atomic Bose-Einstein
condensates interact via
short-range s-wave interactions which decay as 1/r 6 (van der Waals interactions).
However, recently a BEC of chromium atoms was made by T. Pfau's group in Stuttgart [PRL
94, 160401 (2005)]. Chromium has an anomalously large magnetic dipole moment and
consequently a chromium BEC has large dipole-dipole interactions. There are also many
efforts going on worldwide to make ultracold polar molecules which have potentially huge
dipole moments. In this talk I will introduce the theory of trapped dipolar condensates
and compare it to the results of experiments conducted so far. We shall see how the
long-range and anisotropic form of the dipole-dipole interaction leads to new mesoscopic
effects which depend on the shape of the condensate surface. These include
magnetotstriction and an instability towards the formation of a density wave. Finally, I
will dicuss the role of the sign of the interactions in controlling the properties of
these novel superfluids under rotation.