The study of cloud cover changes during Forbush decreases in galactic cosmic rays (GCR) and Earth transits of the Heliospheric Current Sheet (HCS) allow the investigation of the impact of solar variability on the Earth's atmosphere at short timescales and theoretically free of. natural internal modes of climate variability with similar temporal characteristics. This paper reviews the recent research that has examined the cloud cover responses coincident with Forbush decreases and Earth transits of HCS. In particular the studies have used data from the International Satellite Cloud Climatology Project (ISCCP) and have explored the global pattern of changes in cloud. The studies have consistently revealed substantial reductions in high-level cloud over high geomagnetic latitudes, especially of the southern hemisphere. However, unfortunately the largest cloud anomalies occur where the accuracy of the ISCCP cloud retrievals is likely to be the lowest. Thus the paper explores the supporting and contradictory evidence for the existence of these cloud responses and their relation to some of the proposed mechanisms linking solar variability with the Earth's climate.