The existence of a significant non-baryonic component to the Universe is widely accepted, with worldwide efforts underway trying to detect this so-called dark matter. The ZEPLIN-III detector utilises liquid xenon (Xe) as a target medium in the search for the expected rare interactions of Weakly Interacting Massive Particles, or WIMPs, with ordinary baryonic matter. The neutralino, arising in supersymmetric extensions to the standard model of particle physics, provides a particularly well-motivated candidate. The ZEPLIN-III experiment, operating in two-phase (liquid/gas) mode, measures both the scintillation and ionisation signatures produced during an interaction. The first science run (FSR) of ZEPLIN-III was performed during three months in 2008. The run culminated in a published result which excluded a WIMP-nucleon interaction cross-section above 8:1 x 10-8 pb for a 60 GeVc-2 WIMP at the 90% confidence level. ZEPLIN-III then entered an upgrade period where the photomultiplier tube (PMT) array, previously the dominant source of background, was replaced with new, ultra-low background, PMTs. The radio-contamination of components used to make these PMTs has been thoroughly studied and their impact on the background rates in ZEPLIN-III characterised. Additionally, a new 1.5 tonne plastic scintillator veto detector was constructed, increasing the ability to reject WIMPlike signals caused by neutron induced nuclear recoil events and improving the γ-ray discrimination capability of ZEPLIN-III. The second science run (SSR) of ZEPLIN-III began in June 2010 and continued for 6 months, with a projected upper limit for the interaction cross-section of 1:52 x 10-8 pb for a 55 GeVc-2 WIMP at the 90% confidence level.