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: (1) magnetic feedback on the flow, (2) stochastic forcing, and (3) 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.

太阳周期的一个明显特征是它从一个周期到另一个周期的变化。在本文中，我们回顾了太阳周期长期变化的发电机模型。长期变化是指超过 11 年周期的周期调制，其中包括格涅维舍夫-奥尔/偶-奇规则、极大极小值、极大极大值、格莱斯伯格循环和苏斯循环。在对观测数据进行简要回顾后，我们提出了太阳周期的发电机模型。通过仔细分析发电机模型和观察到的数据，我们确定了以下调制的广泛原因：（1）流动的磁反馈，（2）随机强迫，以及（3）发电机各个过程中的时间延迟。为了证明这些原因中的每一个，我们提出了一些循环调制说明性模型的结果，并讨论了它们的优点和缺点。我们还讨论了一些关键问题及其当前趋势。本文最后讨论了我们目前对比较磁循环的详细特征和发电机模型的大尺度速度与稳健观测的无知状态。