  Solar activity has a cyclic nature with the ~11-year Schwabe cycle dominating
its variability on the interannual timescale. However, solar cycles are
significantly modulated in length, shape and magnitude, from near-spotless
grand minima to very active grand maxima. The ~400-year-long direct
sunspot-number series is inhomogeneous in quality and too short to study robust
parameters of long-term solar variability. The cosmogenic-isotope proxy extends
the timescale to twelve millennia and provides crucial observational
constraints of the long-term solar dynamo modulation. Here, we present a brief
up-to-date overview of the long-term variability of solar activity at
centennial--millennial timescales. The occurrence of grand minima and maxima is
discussed as well as the existing quasi-periodicities such as centennial
Gleissberg, 210-year Suess/de Vries and 2400-year Hallstatt cycles. It is shown
that the solar cycles contain an important random component and have no
clock-like phase locking implying a lack of long-term memory. A brief yet
comprehensive review of the theoretical perspectives to explain the observed
features in the framework of the dynamo models is presented, including the
nonlinearity and stochastic fluctuations in the dynamo. We keep gaining
knowledge of the processes driving solar variability with the new data
acquainted and new models developed.
