We present results of a multi-wavelength program to study the faint discrete X-ray source population discovered by Chandra in the Galactic Centre (GC). From IR imaging obtained with the VLT we identify candidate K-band counterparts to 75% of the X-ray sources in our sample. By combining follow-up VLT K-band spectroscopy of a subset of these candidate counterparts with the magnitude limits of our photometric survey, we suggest that only a small percentage of the sources are HMXBs, while the majority are likely to be canonical LMXBs and CVs at the distance of the GC. In addition, we present our discovery of highly structured small-scale (5-15) extinction towards the Galactic Centre. This is the finest-scale extinction study of the Galactic Centre to date. Finally, from these VLT observations we are able to place constraints on the stellar counterpart to the ``bursting pulsar GRO J1744-28.