Given any finite graph $G$, define the bunkbed graph as $\tilde G=G\times K_2$, where $K_2$ consists of two vertices $\{0,1\}$ connected by an edge. In edge percolation every edge in $G \times K_2$ is present with probability $p$. An old conjecture (dating at least to Kateleyn 1985) states that for all $G$ and $p$ the probability that $(u,0)$ is in the same component as $(v,0)$ is greater than the probability that $(u,0)$ is in the same component as $(v,1)$ for every pair of vertices $u,v$ in $G$. I will discuss what is known about this conjecture.