Surgical data science is revolutionizing minimally invasive surgery by enabling context-aware applications. However, many challenges exist around surgical data (and health data, more generally) needed to develop context-aware models. This work - presented as part of the Endoscopic Vision (EndoVis) challenge at the Medical Image Computing and Computer Assisted Intervention (MICCAI) 2020 conference - seeks to explore the potential for visual domain adaptation in surgery to overcome data privacy concerns. In particular, we propose to use video from virtual reality (VR) simulations of surgical exercises in robotic-assisted surgery to develop algorithms to recognize tasks in a clinical-like setting. We present the performance of the different approaches to solve visual domain adaptation developed by challenge participants. Our analysis shows that the presented models were unable to learn meaningful motion based features form VR data alone, but did significantly better when small amount of clinical-like data was also made available. Based on these results, we discuss promising methods and further work to address the problem of visual domain adaptation in surgical data science. We also release the challenge dataset publicly at https://www.synapse.org/surgvisdom2020.