In this review we discuss the occurrence and statistical properties of Grand minima based on the available data covering the last millennia. In particular, we consider the historical record of sunspot numbers covering the last 400 years as well as records of cosmogenic isotopes in natural terrestrial archives, used to reconstruct solar activity for up to the last 11.5 millennia, i.e. throughout the Holocene. Using a reconstruction of solar activity from cosmogenic isotope data, we analyze statistics of the occurrence of Grand minima. We find that: the Sun spends about most of the time at moderate activity, 1/6 in a Grand minimum and some time also in a Grand maximum state; Occurrence of Grand minima is not a result of long-term cyclic variations but is defined by stochastic/chaotic processes; There is a tendency for Grand minima to cluster with the recurrence rate of roughly 2000-3000 years, with a weak ≈210-yr periodicity existing within the clusters. Grand minima occur of two different types: shorter than 100 years (Maunder-type) and long ≈150 years (Spörer-type). It is also discussed that solar cycles (most possibly not sunspots cycle) could exist during the Grand minima, perhaps with stretched length and asymmetric sunspot latitudinal distribution.
These results set new observational constraints on long-term solar and stellar dynamo models.