For a given class ${\cal F}$ of uniform frames of fixed redundancy we define a
Grassmannian frame as one that minimizes the maximal correlation $|< f_k,f_l >|$
among all frames $\{f_k\}_{k \in {\cal I}} \in {\cal F}$. We first analyze
finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and
antipodal spherical codes we derive bounds on the minimal achievable correlation for
Grassmannian frames. These bounds yield a simple condition under which Grassmannian frames
coincide with uniform tight frames. We exploit connections to graph theory, equiangular
line sets, and coding theory in order to derive explicit constructions of Grassmannian
frames. Our findings extend recent results on uniform tight frames. We then introduce
infinite-dimensional Grassmannian frames and analyze their connection to uniform tight
frames for frames which are generated by group-like unitary systems. We derive an example
of a Grassmannian Gabor frame by using connections to sphere packing theory. Finally we
discuss the application of Grassmannian frames to wireless communication and to multiple
description coding.