  The light distribution in the disks of many galaxies is non-axisymmetric or
`lopsided' with a spatial extent much larger along one half of a galaxy than
the other, as in M101. Recent near-IR observations show that lopsidedness is
common. The stellar disks in nearly 30 % of galaxies have significant
lopsidedness, greater than 10 % measured as the Fourier amplitude of the m=1
component normalized to the average value. This asymmetry is traced
particularly well by the atomic hydrogen gas distribution lying in the outer
parts. The lopsidedness also occurs in the nuclear regions, where the nucleus
is offset with respect to the outer isophotes. The galaxies in a group
environment show higher lopsidedness. The origin of lopsidedness could be due
to the disk response to a tidally distorted halo, or via gas accretion. The
lopsidedness has a large impact on the dynamics of the galaxy, its evolution,
the star formation in it, and on the growth of the central black hole and on
the nuclear fueling, merging of binary black holes etc. The disk lopsidedness
can be used as a diagnostic to study the halo asymmetry. This is an emerging
area in galactic structure and dynamics. In this review, the observations to
measure the lopsided distribution, as well as the theoretical progress made so
far to understand its origin and properties, and the related open problems will
be discussed. (abridged).
