Robbins was born in Grayson, Georgia, and educated at Rocky Mount High School in Rocky Mount, North Carolina. Robbins began his career as an application developer for North Carolina National Bank. He later joined Wellfleet Communications, which merged with SynOptics to become Bay Networks, followed by a brief tenure at Ascend Communications. He joined Cisco in 1997, filling the roles of senior vice president of the Americas and senior vice president of Worldwide Field Operations. As CEO, Robbins became noted for accelerating the pace of Cisco's modern growth while disrupting outdated working modes; promoting employee trust based in transparency of policy and process; and humanitarian policies and workplace diversity.