  A introductory review to emergent noncommutative gravity within Yang-Mills
Matrix models is presented. Space-time is described as a noncommutative brane
solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on
the brane arise as fluctuations of the bosonic resp. fermionic matrices around
such a background, and couple to an effective metric interpreted in terms of
gravity. Suitable tools are provided for the description of the effective
geometry in the semi-classical limit. The relation to noncommutative gauge
theory and the role of UV/IR mixing is explained. Several types of geometries
are identified, in particular "harmonic" and "Einstein" type of solutions. The
physics of the harmonic branch is discussed in some detail, emphasizing the
non-standard role of vacuum energy. This may provide new approach to some of
the big puzzles in this context. The IKKT model with D=10 and close relatives
are singled out as promising candidates for a quantum theory of fundamental
interactions including gravity.
