  The two-dimensional causal dynamical triangulations ($2$d CDT) is a lattice
model of quantum geometry. In $2$d CDT, one can deal with the quantum effects
analytically and explore the physics through the continuum limit. The continuum
theory is known to be two-dimensional projectable Horava-Lifshitz quantum
gravity ($2$d projectable HL QG). In this chapter, we wish to review the very
relation between $2$d CDT and $2$d projectable HL QG in detail.
