Long-term correlations between optical, infrared and X-ray observations of X-ray binaries

X-ray binaries radiate brightly from radio to X-ray due to the accretion and ejection of matter in the system. There are complex, correlated flux variations that probe links between emitting components. Studying the nature of accretion onto these compact objects sheds light on several broad fields in astrophysics. This is why multi-wavelength monitoring campaigns of these outbursts are becoming increasingly popular. Here I briefly review the progression of multi-wavelength studies of X-ray binaries, focusing on long-term (day+ timescales) correlated behaviour between optical/infrared and X-ray emission. A tight power law correlation exists between optical/IR and X-ray fluxes in the hard state, which can be explained with a combination of disc and jet optical/IR emission. For most cases this is essentially an optical disc - X-ray corona relation. Black hole systems are systematically optically brighter at a given X-ray luminosity compared to neutron stars. This is found to be due to different disc sizes, compact object masses, more jet emission for black holes, and a bolometric X-ray correction. The optical - X-ray correlation can be used to constrain the nature of the compact object for new X-ray transients. We present new optical/IR - X-ray correlations in several X-ray binaries (using X-ray Swift, MAXI, NICER and HXMT data), including MAXI J0556-332, Swift J1910.2-0546, MAXI J1820+070 and MAXI J1348-630. In SAX J1808.4-3658 we find an optical - X-ray anti-correlation during its re-flare period, which is likely a positive correlation with a time delay. We demonstrate that using these correlations in conjunction with spectral energy distributions and colour-magnitude diagrams (and in some cases polarimetry and fast timing studies) can successfully isolate the different emitting components in order to measure accurate outer disc temperatures and jet synchrotron spectral indices. Optical/IR monitoring of X-ray binaries is essential to these efforts; we have been monitoring $\sim$ 40-50 X-ray binaries with the Faulkes Telescopes / Las Cumbres Observatory (LCO) global robotic network for 1.5 decades. We present optical light curves and optical - X-ray correlations for several outbursts. We also find evidence for low level, variable accretion activity and long-term trends in quiescence in some systems. We will also introduce our new real-time optical monitoring pipeline, the "X-ray Binary New Early Warning System (XB-NEWS)", which aims to detect and announce new X-ray binary outbursts within a day of first optical detection. We are now detecting the early stages of these outbursts with our optical telescopes, before they become bright enough for X-ray detection. This allows us to trigger X-ray and multi-wavelength campaigns during the very early stages of outbursts, to constrain the outburst triggering mechanism. Disc instability models predict that for X-ray binaries in quiescence, there should be a brightening of the optical flux prior to an X-ray outburst. Tracking the X-ray variations of XRBs in quiescence is generally not possible, so optical monitoring provides the best means to measure the mass accretion rate variability between outbursts. Multi-wavelength work of X-ray binaries is booming, but could still be in its infancy. With SKA, LSST and various upcoming X-ray missions, the golden age may be yet to come.