  The aim of this paper is to give a basic overview of Deformation Quantization
(DQ) to physicists. A summary is given here of some of the key developments
over the past thirty years in the context of physics, from quantum mechanics to
quantum field theory. Also, we discuss some of the conceptual advantages of DQ
and how DQ may be related to algebraic quantum field theory. Additionally, our
previous results are summarized which includes the construction of the Fedosov
star-product on dS/AdS. One of the goals of these results was to verify that DQ
gave the same results as previous analyses of these spaces. Another was to
verify that the formal series used in the conventional treatment converged by
obtaining exact and nonperturbative results for these spaces.
