Short and long-term variability of solar cycle and fluctuations of dynamo drivers Dmitry Sokoloff1,2 1 Department of Physics, Moscow State University, Moscow, Russia 2 IZMIRAN, Moscow, Russia Cyclic solar activity is far to be just a sinusoidal oscillations. Shape of activity wave underlying by a wave of quasistationary magnetic field varies from one cycle to the other. Moreover, from time to time catastrophyc events like Maunder minimum and other Grand minima occur. A short presentation of available observations for this variability is given. The cycle is supported by solar dynamo based on a joint action of mirror-asymmetric convection and differential rotation. The dynamo drivers being spatial averaging of noisy quantities contain some random contributions. Contemporary ideas concerning possible amplitude of such noisy contributions are considered. We argue that these noisy contributions can be sufficient to explain the observed variability of solar cycle.