Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve hyperbolic PDEs describing wavelike phenomena, such as fluid flow. In front-tracking SDG methods, the inclined facets of spacetime elements are aligned with the trajectories of moving domain boundaries, phase interfaces, and other singular surfaces. These methods are particularly effective because SDG solution fields naturally accommodate the jumps that occur at singular surfaces. Our goal is to construct front-tracking tetrahedral meshes in 2D×time that partition a spacetime analysis domain Ω ⊂ E × R while satisfying a causality condition that facilitates the SDG solution procedure. Trajectories of ∂Ω and of interior singular surfaces are generally solution-dependent and must be computed as the solution evolves.