We introduce a series of ‘minimal’ models to describe a common light-driven directional solidification process, known as frontal photopolymerization (FPP), focusing on experimental observables: the solidification kinetics, light attenuation and spatiotemporal monomer-to-polymer conversion. Specifically, we focus on FPP propagation that yields conversion profiles that are not invariant with time, and which cannot be simply described by the presence of mass or heat diffusion. The models are assessed against experimental data for the photopolymerization of a model trimethacrylate system. We find that the simplest model, comprising a single equation of motion for the conversion fraction ϕ and a generalized Beer–Lambert law, can only describe the experimental data by assuming an unphysical variation in optical absorption. Introducing a ϕ-dependent reaction constant Keff is found to require a time dependence, regardless of the functional form in ϕ. We conclude by introducing a ‘minimal’ chemical model, which is based on a simple three-step reaction scheme involving the spatiotemporal evolution of the photoinitiator fraction, relative fraction of radicals and monomer conversion fraction, that is able to capture the experimental data with a small number of parameters and under reasonable FPP assumptions. Our framework provides important predictive ability for ubiquitous solidification and patterning processes, including three-dimensional printing, via photopolymerization.