  We study the origins of the five ten-dimensional ``matrix superstring''
theories, supplementing old results with new ones, and find that they all fit
into a unified framework. In all cases the matrix definition of the string in
the limit of vanishingly small coupling is a trivial 1+1 dimensional infra-red
fixed point (an orbifold conformal field theory) characterized uniquely by
matrix versions of the appropriate Green-Schwarz action. The Fock space of the
matrix string is built out of winding T-dual strings. There is an associated
dual supergravity description in terms of the near horizon geometry of the
fundamental string solution of those T-dual strings. The singularity at their
core is related to the orbifold target space in the matrix theory. At
intermediate coupling, for the IIB and SO(32) systems, the matrix string
description is in terms of non-trivial 2+1 dimensional fixed points. Their
supergravity duals involve Anti de-Sitter space (or an orbifold thereof) and
are well-defined everywhere, providing a complete description of the fixed
point theory. In the case of the type IIB system, the two extra organizational
dimensions normally found in F-theory appear here as well. The fact that they
are non-dynamical has a natural interpretation in terms of holography.
