Hybrid percolation is a random graph on the vertex set $V= \mathbb{Z}^{d}\times [N]$ in which vertices $(x,k)$ and $(y,l)$ are connected with probability $p_{N}$ if $x$ and $y$ are neighboring vertices of the lattice $\mathbb{Z}^{d}$. The percolation graph is the skeleton of a spatial epidemic that evolves as follows: (a) infected individuals, represented by vertices of the graph, remain infected for one unit of time, after which they recover and acquire permanent immunity from further infection; and (b) infected individuals infect susceptible individuals (vertices at neighboring sites of $\mathbb{Z}^{d}$) with probability $p_{N}$. We shall describe results concerning the scaling limits of both the percolation graph and the associated epidemic process as $N$ becomes large in the critical regime $p_{N} = 1/(2dN)$.