We will discuss new estimates for the size and structure of the nodal set $\{u=0\}$ and the singular set $\{u=|\nabla u|=0\}$ of solutions to parabolic inequalities with parabolic Lipschitz coefficients. In particular, we show that almost all of these sets are covered by regular parabolic Lipschitz graphs, with quantitative control, and that both satisfy parabolic Minkowski bounds depending only on a doubling quantity at a point. Many of these results are new even in the case of the heat equation on $\mathbb{R}^n\times \mathbb{R}$. This is joint work with Max Hallgren and Zilu Ma.