This thesis studies the critical properties of several systems under the overarching theme of active matter. These are systems that constantly consume energy at particle level and transform it into motion. Several field theories have been proposed as continuum descriptions of isotropic systems of self-propelled particles, that are able to reproduce some of the phenomena observed in these systems at particle level, mainly motility-induced phase separation (MIPS). This is a form of phase separation in the absence of attractive interactions that is not present in these systems' passive counterparts. These theories are built as extensions of models of equilibrium phase separation (Model B) that minimally break detailed balance.

This thesis addresses the question of how these field theories behave at criticality, in the transition between uniform and phase separated states, and whether this transition lies in the Ising-like universality class of the background equilibrium model, or instead belongs to a new universality class.

The first model analysed, named here conserved KPZ+, is a simplification of the main MIPS model studied, and proves to be a general model for surface growth with conserved mass, not present in the literature. This system has an Renormalization Group flow that, to one loop, shows a strong coupling regime in and above its critical dimension d_c = 2 that was not present in the previous systems considered to model this physical process. This strong coupling regime is also explored numerically, showing that the equation of motion indeed has a more complex phase diagram than it was thought for these surfaces.

The full field theory for MIPS is then analysed using Renormalization Group. The results are that, between 2 and 4 dimensions, a new fixed point appears as an extension of the Wilson-Fisher fixed point. This new fixed point rules a new transition to a strong coupling regime not present in the equilibrium Model B. The perturbative nature of the RG approach leaves the quantitative characterization of this phase as an open question, but the phase diagram obtained matches roughly the one explored numerically in the literature, and strongly suggests that the strong coupling regime represents a new universality class of nonequilibrium phase separation.

Finally, the entropy production rate (EPR) is studied for these active field theories close to the equilibrium critical points. The results indicate that the EPR per correlation volume can be constant or even diverge close to the equilibrium critical points, meaning that even though the dynamics of these systems are effectively in equilibrium, there is a nontrivial critical scaling for the EPR that is part of Ising-like universality classes.