Intense positron beams are under development or being considered at se
veral laboratories. Already today a few accelerator based high intensi
ty, low brightness e(+) beams exist producing of the order of 10(8)- 1
0(9) e(+)/s. Several laboratories are aiming at high intensity, high b
rightness e(+) beams with intensities greater than 10(9) e(+)/s and cu
rrent densities of the order of 10(13)-10(14) e(+) s(-1) cm(-2). Inten
se e(+) beams can be realized in two ways (or in a combination thereof
) either through a development of more efficient beta(+) moderators or
by increasing the available activity of beta(+) particles. In this re
view we shall mainly concentrate on the latter approach. In atomic phy
sics the main trust for these developments is to be able to measure di
fferential and high energy cross-sections in e(+) collisions with atom
s and molecules. Within solid state physics high intensity, high brigh
tness e(+) beams are in demand in areas such as the re-emission e(+) m
icroscope, two-dimensional angular correlation of annihilation radiati
on, low energy e(+) diffraction and other fields. Intense e(+) beams a
re also important for the development of positronium beams, as well as
exotic experiments such as Bose condensation and Ps liquid studies.