In the past several years there has been enormous progress in Artificial Intelligence (AI), and its technology is now deeply permeating our society in many areas including finance, social media, manufacturing, transportation and healthcare. However, the move to incorporate AI into everyday surgical practice has been a much slower affair. This is despite the huge potential benefits, ranging from increased precision, personalized therapy planning, medical data assimilation, surgery risk assessment, quality assurance and reduced hospital costs. There are several reasons, including regulation, lack of big-data infrastructure, and also the huge complexities in modelling surgical processes with AI. Nevertheless, AI is unquestionably making strong inroads into surgery, and is driven by a large community of researchers and strong industrial interest. In this paper we present an overview for non-specialists in AI of the recent progress that has been made in surgery, and a perspective on the future steps required to achieve broader acceptance and adoption.