  We survey partial geometric designs and investigate their concurrences of
points. The concurrence matrix of a design, which encodes the concurrences of
pairs of points, can be used in the classification of designs in some extent.
An ordinary 2-$(v,k,\lambda)$ design has concurrence $\lambda$ for any pair of
distinct points, and its concurrence matrix is circulant. A partial geometry
has two concurrences $1$ and $0$ and a transversal design TD$_{\lambda}(k, u)$
has two concurrences $\lambda$ and $0$. It is also known that the concurrence
matrix of a partial geometric design can have at most three distinct
eigenvalues, all of which are non-negative integers. In this paper, we show the
existence of other partial geometric designs having two or three distinct
concurrences, and investigate which symmetric circulant matrices are realized
as the concurrence matrices of partial geometric designs. We collect known
sources of partial geometric designs and study their structural characteristics
and construction methods. We then give a list of feasible parameter sets for
partial geometric designs of order up to 12 each of which has a circulant
concurrence matrix. We also consider the combinatorial properties and
constructions of partial geometric designs satisfying these parameter sets.
