Falvey was the first person to complete the Seven Summits twice by reaching the summit of Mount Everest from both the Tibetan (1996) and Nepalese sides (2003). He was expedition leader of the team that saw Clare O'Leary become the first Irish woman to reach the summit of Mount Everest (2003). Other extreme expeditions include walking to the South Pole, crossing South Georgia Island and traversing the Greenland ice cap.