Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. Recently, it was shown that a 4-dimensional expanding universe can emerge in the IKKT matrix model, with another 6 spatial dimensions stabilized at the string scale. This scenario was also explored in the BFSS model, in which case the emerging phase yields a scale-invariant spectrum of scalar and tensor perturbation. In this talk, we will discuss recent progress in understanding these results. More precisely, we will discuss a possible way of obtaining the metric out of the matrices in the IKKT model, and ways to probe symmetry breaking in the BFSS model.