Compulsory figures or school figures were formerly a segment of figure skating, and gave the sport its name. They are the "circular patterns which skaters trace on the ice to demonstrate skill in placing clean turns evenly on round circles". For approximately the first 50 years of figure skating as a sport, until 1947, compulsory figures made up 60 percent of the total score at most competitions around the world. These figures continued to dominate the sport, although they steadily declined in importance, until the International Skating Union (ISU) voted to discontinue them as a part of competitions in 1990. Learning and training in compulsory figures instilled discipline and control; some in the figure skating community considered them necessary to teach skaters basic skills. Skaters would train for hours to learn and execute them well, and competing and judging figures would often take up to eight hours during competitions.

Figure skating jumps are an element of three competitive figure skating disciplines: men's singles, women's singles, and pair skating – but not ice dancing. Jumping in figure skating is "relatively recent". They were originally individual compulsory figures, and sometimes special figures; many jumps were named after the skaters who invented them or from the figures from which they were developed. It was not until the early part of the 20th century, well after the establishment of organized skating competitions, when jumps with the potential of being completed with multiple revolutions were invented and when jumps were formally categorized. In the 1920s Austrian skaters began to perform the first double jumps in practice. Skaters experimented with jumps, and by the end of the period, the modern repertoire of jumps had been developed. Jumps did not have a major role in free skating programs during international competitions until the 1930s. During the post-war period and into the 1950s and early 1960s, triple jumps became more common for both male and female skaters, and a full repertoire of two-revolution jumps had been fully developed. In the 1980s men were expected to complete four or five difficult triple jumps, and women had to perform the easier triples. By the 1990s, after compulsory figures were removed from competitions, multi-revolution jumps became more important in figure skating.