We discuss a range of related problems in high-dimensional percolation. These topics have attracted considerable attention in the past two decades, yet their investigation is far from complete. We discuss the relation between critical high-dimensional percolation clusters and super-processes, oriented percolation, and scaling limits of percolation backbones. We continue to discuss long-range percolation and the asymptotic expansion of the percolation threshold. We close this chapter by describing percolation on non-amenable graphs.