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Bootstrap percolation is a wide class of monotone cellular automata withrandom initial state. In this work we develop tools for studying in fullgenerality one of the three `universality' classes of bootstrap percolationmodels 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 interms of these quantities and successfully apply this link to prove new and oldresults for concrete models such as DTBP and Spiral as well as a generalnon-trivial upper bound. Our approach establishes and exploits a tightconnection between subcritical bootstrap percolation and a suitablegeneralisation of classical oriented percolation, which will undoubtedly be thesource of more results and could provide an entry point for generalpercolationists to bootstrap percolation.  Furthermore, we prove that above a certain critical probability there isexponential decay of the probability of a one-arm event, while below it theevent has positive probability and the expected infection time is infinite. Wealso identify this as the transition of the spectral gap and mean infectiontime of the corresponding kinetically constrained model. Finally, weessentially characterise the noise sensitivity properties at fixed density forthe two natural one-arm events.  In doing so we answer fully or partially most of the open questions asked byBalister, Bollob\'as, Przykucki and Smith (2016)---namely we are concerned withtheir Questions 11, 12, 13, 14 and 17.

$\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications