  Motivated by applications to probabilistic cellular automata (PCA) and
bootstrap percolation (BP), we consider a generalised oriented site percolation
model (GOSP) on $\mathbb{Z}^d$. We provide a broad user-oriented overview on
the supercritical regime of this model with little to no proofs. Although not
particularly novel for specialists on standard oriented percolation (OP), from
the point of view of PCA and BP almost all results presented are new and some
rectify previous works. Despite the resemblance with OP, some important
difficulties arise for GOSP. Although we work with GOSP for simplicity, many of
the techniques are much more general, so we hope that the survey will be of use
in different settings.
