  One obvious feature of the solar cycle is its variation from one cycle to
another. In this article, we review the dynamo models for the long-term
variations of the solar cycle. By long-term variations, we mean the cycle
modulations beyond the 11-year periodicity and these include, the
Gnevyshev-Ohl/Even-Odd rule, grand minima, grand maxima, Gleissberg cycle, and
Suess cycles. After a brief review of the observed data, we present the dynamo
models for the solar cycle. By carefully analyzing the dynamo models and the
observed data, we identify the following broad causes for the modulation: (i)
magnetic feedback on the flow, (ii) stochastic forcing, and (iii) time delays
in various processes of the dynamo. To demonstrate each of these causes, we
present the results from some illustrative models for the cycle modulations and
discuss their strengths and weakness. We also discuss a few critical issues and
their current trends. The article ends with a discussion of our current state
of ignorance about comparing detailed features of the magnetic cycle and the
large-scale velocity from the dynamo models with robust observations.
