The first reports on a slow earthquake were for an event in the Izu peninsula, Japan, on an intraplate, seismically active fault. Since then, many slow earthquakes have been detected. It has been suggested that the slow events may trigger ordinary earthquakes (in a context supported by numerical modelling), but their broader significance in terms of earthquake occurrence remains unclear. Triggering of earthquakes has received much attention: strain diffusion from large regional earthquakes has been shown to influence large earthquake activity, and earthquakes may be triggered during the passage of teleseismic waves, a phenomenon now recognized as being common. Here we show that, in eastern Taiwan, slow earthquakes can be triggered by typhoons. We model the largest of these earthquakes as repeated episodes of slow slip on a reverse fault just under land and dipping to the west; the characteristics of all events are sufficiently similar that they can be modelled with minor variations of the model parameters. Lower pressure results in a very small unclamping of the fault that must be close to the failure condition for the typhoon to act as a trigger. This area experiences very high compressional deformation but has a paucity of large earthquakes; repeating slow events may be segmenting the stressed area and thus inhibiting large earthquakes, which require a long, continuous seismic rupture.