  Bootstrap percolation is a wide class of monotone cellular automata with
random initial state. In this work we develop tools for studying in full
generality one of the three `universality' classes of bootstrap percolation
models in two dimensions, termed subcritical. We introduce the new notion of
`critical densities' serving the role of `difficulties' for critical models,
but adapted to subcritical ones. We characterise the critical probability in
terms of these quantities and successfully apply this link to prove new and old
results for concrete models such as DTBP and Spiral as well as a general
non-trivial upper bound. Our approach establishes and exploits a tight
connection between subcritical bootstrap percolation and a suitable
generalisation of classical oriented percolation, which will undoubtedly be the
source of more results and could provide an entry point for general
percolationists to bootstrap percolation.
  Furthermore, we prove that above a certain critical probability there is
exponential decay of the probability of a one-arm event, while below it the
event has positive probability and the expected infection time is infinite. We
also identify this as the transition of the spectral gap and mean infection
time of the corresponding kinetically constrained model. Finally, we
essentially characterise the noise sensitivity properties at fixed density for
the two natural one-arm events.
  In doing so we answer fully or partially most of the open questions asked by
Balister, Bollob\'as, Przykucki and Smith (2016)---namely we are concerned with
their Questions 11, 12, 13, 14 and 17.
