In this paper we present rigorous results on the critical behavior of the Activated Random Walk model. We conjecture that on a general class of graphs, including $$\mathbb Z^d$$ Z d , and under general initial conditions, the system at the critical point does not reach an absorbing state. We prove this for the case where the sleep rate $$\lambda $$ λ is infinite. Moreover, for the one-dimensional asymmetric system, we identify the scaling limit of the flow through the origin at criticality. The case $$\lambda < + \infty $$ λ < + ∞ remains largely open, with the exception of the one-dimensional totally-asymmetric case, for which it is known that there is no fixation at criticality.