We present the results of concurrent X-ray and optical monitoring of the Seyfert 1 galaxy Mrk 79 over a period of more than five years. We find that on short to medium time-scales (days to a few tens of days) the 2-10 keV X-ray and optical u and V band fluxes are significantly correlated, with a delay between the bands consistent with zero days. We show that most of these variations may be well reproduced by a model where the short-term optical variations originate from reprocessing of X-rays by an optically thick accretion disc. The optical light curves, however, also display long time-scale variations over thousands of days, which are not present in the X-ray light curve. These optical variations must originate from an independent variability mechanism and we show that they can be produced by variations in the (geometrically) thin disc accretion rate as well as by varying reprocessed fractions through changes in the location of the X-ray corona.