The recent developments towards the possible non-perturbative formulation o
f string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are
discussed. In the first part, we give a critical review on the status of ou
r present understanding, focusing on the connection of the D0-brane matrix
models to supergravity and its relevance to the so-called Matrix-theory con
jecture. We also discuss some problems concerning the conjectured relation
between supergravity in AdS background and SYM fr om the viewpoint of D-bra
ne interactions. We present a qualitative argument showing how the boundary
condition at AdS boundary dictates the correlators on the large N system o
f source D-branes. Then, in the final part, we turn to the question how to
formulate the condensation of graviton in matrix models, taking the simples
t example of type IIB matrix model. We argue the emergence of a hidden symm
etry GL(10, R), beyond the manifest Lorentz symmetry SO(9, 1), by embedding
U(N) model into models with higher N and by treating the whole recursive s
eries of models simultaneously. This suggests a possible approach toward ba
ckground independent formulations of matrix models.