  A configuration p in r-dimensional Euclidean space is a finite collection of
labeled points p^1,p^2,...,p^n in R^r that affinely span R^r. Each
configuration p defines a Euclidean distance matrix D_p = (d_ij) =
(||p^i-p^j||^2), where ||.|| denotes the Euclidean norm. A fundamental problem
in distance geometry is to find out whether or not, a given proper subset of
the entries of D_p suffices to uniquely determine the entire matrix D_p. This
problem is known as the universal rigidity problem of bar frameworks. In this
chapter, we present a unified approach for the universal rigidity of bar
frameworks, based on Euclidean distance matrices (EDMs), or equivalently, on
projected Gram matrices. This approach makes the universal rigidity problem
amenable to semi-definite programming methodology. Using this approach, we
survey some recently obtained results and their proofs, emphasizing the case
where the points p^1,...,p^n are in general position.
