We present the results of a deep imaging survey of the Virgo cluster of galaxies , concentrated around the cores of Virgo subclusters A and B . The goal of this survey was to detect and study very low surface brightness features present in Virgo , including discrete tidal features , the faint halos of luminous galaxies , and the diffuse intracluster light ( ICL ) . Our observations span roughly 16 degrees ^ { 2 } in two filters , reaching a 3 \sigma limiting depth of \mu _ { B } =29.5 and \mu _ { V } =28.5 mag arcsec ^ { -2 } . At these depths , our limiting systematic uncertainties are astrophysical : variations in faint background sources as well as scattered light from galactic dust . We show that this dust-scattered light is well-traced by deep far-infrared imaging , making it possible to separate it from true diffuse light in Virgo . We use our imaging to trace and measure the color of the diffuse tidal streams and intracluster light in the Virgo core near M87 , in fields adjacent to the core including the M86/M84 region , and to the south of the core around M49 and subcluster B , along with the more distant W ^ { \prime } cloud around NGC 4365 . Overall , the bulk of the projected ICL is found in the Virgo core and within the W ^ { \prime } cloud ; we find little evidence for an extensive ICL component in the field around M49 . The bulk of the ICL we detect is fairly red in color ( B - V =0.7–0.9 ) , indicative of old , evolved stellar populations . Based on the luminosity of the observed ICL features in the cluster , we estimate a total Virgo ICL fraction of 7–15 % . This value is somewhat smaller than that expected for massive , evolved clusters , suggesting that Virgo is still in the process of growing its extended ICL component . We also trace the shape of M87 ’ s extremely boxy outer halo out to \sim 150 kpc , and show that the current tidal stripping rate from low luminosity galaxies is insufficient to have built M87 ’ s outer halo over a Hubble time . We identify a number of previously unknown low surface brightness structures around galaxies projected close to M86 and M84 . The extensive diffuse light seen in the infalling W ^ { \prime } cloud around NGC 4365 is likely to be subsumed in the general Virgo ICL component once the group enters the cluster , illustrating the importance of group infall in generating intracluster light . Finally , we also identify another large and extremely low surface brightness ultra-diffuse galaxy , likely in the process of being shredded by the cluster tidal field . With the survey complete , the full imaging dataset is now available for public release .