A possible mechanism of solar variability influence upon the Earth's climate is related to a link between the cosmic ray flux and cloudiness. Here we review evidences relating terrestrial climate variability to changes of cosmic ray flux in the Earth's vicinity on different time scales. On daily scales, major Forbush decreases and solar energetic particle events can affect the cyclogenesis in sub-polar regions. At inter-annual scales, a significant correlation between low clouds and cosmic ray induced ionization has been found. Different climate reconstructions depict a correlation with variations of the geomagnetic field intensity throughout the last millennia, providing additional support to a systematic effect of cosmic rays. On very long time scales, a close relation was reported between the global climate and variations of cosmic ray flux expected from local galactic environment changes. Although none of these facts alone is conclusive, in the aggregate they strongly support the link between cosmic rays and climate on Earth. These links are based on phenomenological relations, and theoretical development and experimental investigation of this hypothesis is ongoing.