  This is a review of the properties of 2d quantum quasiperiodic
antiferromagnets as reported in studies that have been carried out in the last
decade. Many results have been obtained for perfectly ordered as well as for
disordered two dimensional bipartite quasiperiodic tilings. The theoretical
methods used include spin wave theory, and renormalization group along with
Quantum Monte Carlo simulations. These methods all show that the ground state
of these unfrustrated antiferromagnets have N\'eel type order but with a highly
complex spatial distribution of local staggered magnetization. The ground state
properties, excitation energies and spatial dependence, structure factor, and
local susceptibilities are presented. The effects of introducing geometrical
disorder on the magnetic properties are discussed.
