Liouville theory in its timelike regime is an interesting model of two-dimensional gravity because it reproduces the characteristic minus sign of the conformal-factor kinetic term of higher-dimensional Einstein-Hilbert gravity. In this talk, I will first present a proposal for two-dimensional quantum gravity with a cosmological constant based on the conformal bootstrap results of timelike Liouville theory coupled to unitary conformal matter. The spectrum of physical energies is obtained from the BRST cohomology of diffeomorphisms, and the 4-point function of states belonging to this spectrum is finite and crossing symmetric. I will then present the perturbative computation of the gravitational partition function around the sphere saddle and discuss a proposal for an all orders result. Finally, time permitting, I will discuss some work in progress on timelike Liouville with a conformal boundary.