The field of surgical procedures has undergone a significant transformation in the last three decades with the introduction of robotic surgery. In operating rooms, robotic devices are now integrated into the planning and execution of surgical treatments with advantages over traditional laparoscopy, such as enhanced dexterity, improved ergonomics, motion scaling, and effective tremor filtering. Over the past decade, robotic systems, particularly the da Vinci robotic system from Intuitive Surgical Inc. in Sunnyvale, CA, have played a pivotal role in minimally invasive robot-assisted procedures. Despite these advancements, surgical robotics still has limitations: surgical procedures' success robustly depends on the surgeon’s ability, and the minimal access to the surgeon field brings a heavy mental workload to surgeons. At the same time, the surgical environment is strongly unstructured and prone to complications. For this reason, there is the need for advanced assistive control features capable of augmenting surgeon’s skills and facilitating autonomous execution of surgical tasks to ensure consistently high-quality intervention. As surgical robotics moves towards increased autonomy, vision-based techniques, haptics and data-driven algorithms constitute key concepts in robotic scenarios. This thesis aims to address the limitations of surgical robotics by contributing to different levels of autonomy of surgical robotic procedures. Each chapter of the thesis examines part of the research work conducted during the Ph.D. and concerns one or more of the many fields that contribute to robotics automation.