The science of dendrochronology allows us to assign precise years to individual tree rings, making such samples ideal calibration sources for radiocarbon dating. Recently, single-year radiocarbon measurements have allowed Miyake et al. (2012) to identify a 12% increase in radiocarbon in 774-775 AD, and another such event in 993-994 AD (Miyake et al., 2013). In this talk, presenting work in collaboration with Mike Dee (Oxford/Groningen), I will show that we do not observe such signals in years corresponding to known historical supernovae, briefly review evidence that these Miyake events may have a solar origin, demonstrate how Bayesian models can help us discover more of them, and discuss how they can be used both for archaeological dating and solar and stellar physics.