  We review recent developments in the type IIB matrix model, which was
conjectured to be a nonperturbative formulation of superstring theory. In the
first part we review the recent results for the Euclidean model, which suggest
that SO(10) symmetry is spontaneously broken. In the second part we review the
recent results for the Lorentzian model. In particular, we discuss Monte Carlo
results, which suggest that (3+1)-dimensional expanding universe emerges
dynamically. We also discuss some results suggesting the emergence of
exponential expansion and the power-law expansion at later times. The behaviors
at much later times are studied by the classical equation of motion. We discuss
a solution representing 3d expanding space, which suggests a possible solution
to the cosmological constant problem.
