  An introduction to the defects which dominate the physics of superfluid
He$^4$ films, of superconducting slabs and of crystalline and hexatic membranes
is given. We first review point vortices in two-dimensional neutral superfluids
and discuss the unusual screening which arises when the bosons are charged, as
in superconducting films. Dislocation and disclination defects in crystalline
membranes are discussed from a similar point of view. There is little or no
screening in ``monolayer'' crystals, which are strongly constrained to lie in a
flat two-dimensional plane. A strong nonlinear screening effect arises,
however, in 2d membranes allowed to buckle into the third dimension. This
screening drastically lowers dislocation and disclination energies, and forces
crystalline membranes to melt at any finite temperature. We point out that
buckled 5- and 7-fold disclinations in hexatic membranes have in general
different logarithmically divergent energies. A similar asymmetry exists in the
energies of 5- and 7-fold defects in {\it liquid} membranes. This difference
determines the sign of the Gaussian bending rigidity, and has important
consequences in membranes which can change their topology or with free boundary
conditions.
