  The type IIB matrix model, also known as the IKKT model, has been proposed as
a promising candidate for a non-perturbative formulation of superstring theory.
Based on this proposal, various attempts have been made to explain how our
four-dimensional space-time can emerge dynamically from superstring theory. In
this article, we review the progress in numerical studies on the type IIB
matrix model. We particularly focus on the most recent results for the
Euclidean and Lorentzian versions, which are obtained using the complex
Langevin method to overcome the sign problem. We also review the earlier
results obtained using conventional Monte Carlo methods and clarify the
relationship among different calculations.
