Although the occurrence of many comets had been recorded, it was not until 1577 that the Danish astronomer Tycho Brahe suggested that they traveled in elongated rather than circular orbits. A century later Giovanni Borelli concluded that the orbits were parabolic and that comets passed through the solar system but once, never to return. In 1705, however, Edmond Halley concluded that the comet observed in 1682 was the same one that had been described in 1531 and 1607, and he predicted that it would return again in late 1758 or early 1759. The comet was sighted on Christmas Day in 1758, and it returned again in 1835, 1910, and 1986 (see Halley's comet). While some comets appear to have parabolic orbits (see parabola), others return to the inner solar system in highly elongated orbits with periods ranging from a hundred to thousands of years. Still others return at shorter intervals of less than 10 years and reach aphelion (the orbital point farthest from the sun) near the planet Jupiter; these have been captured into their smaller orbits by Jupiter's gravitational attraction.

A comet far from the sun consists of a dense solid body or conglomerate of bodies a few miles in diameter called the nucleus. As it approaches the sun the nucleus becomes enveloped by a luminous cloud of dust and gases called the coma; this luminosity is caused by the molecules absorbing and reflecting the radiation of the sun. According to the icy-conglomerate theory proposed by F. L. Whipple in 1949, the nucleus consists of frozen water and gases with particles of heavier substances interspersed throughout, thus being in effect a large, dirty snowball, although more recent research has suggested that comets may contain a higher proportion of dust and rock than previously proposed. The Stardust probe—passed near Comet Wild 2 in 2004, collected particles from the coma, and returned the samples to earth in 2006—found evidence that many of the dust particles were formed at high temperatures not found in the Oort cloud and Kuiper belt (see below), where comets are believed to have formed. Data from the Deep Impact mission, which sent a projectile crashing into Comet Tempel 1 in 2005, suggests that suggests that the interior structure of comets may consists of layers of accreted material. As the comet approaches the sun, the solar wind drives particles and gases from the near the surface of the nucleus and coma to form a tail which can extend as much as 100 million mi (160 million km) in length. Thus the tail always streams out in the direction opposite the sun; i.e., it follows the head as the comet approaches the sun and precedes it as the comet passes perihelion (its closest point to the sun) and moves away.

Near the sun a comet can change drastically in size and shape; it may even split into two or more pieces, as Comet Biela did in 1846, and Comet West did in 1976. The comas of comets vary widely in size, some being the size of the earth or larger. However, the nucleus, which makes up virtually all a comet's mass, is small; in 1986 the Giotto and Vega spacecrafts observed Comet Halley's nucleus to be only about 6 mi (10 km) in diameter. Comets lose material and thus brightness with successive passages near the sun. Some of this material moves around the comet's orbit as a stream of meteoroids (see meteor); when the earth passes through this path, a meteor shower is observed.

In 1992 the periodic comet Shoemaker Levy 9 made an extremely close passage of Jupiter. The tidal stresses induced by the giant planet's gravity shattered the comet's nucleus, estimated to have been 5–9 km (3–5 mi) in diameter, into more than 20 major fragments, the largest of which was about 4 km (2.5 mi) in diameter. Two years later, the returning fragmented comet crashed into Jupiter; observations from both terrestrial observatories and artificial satellites such as the Hubble Space Telescope yielded vast amounts of information about the structure of comets and about Jupiter's atmosphere.

In 1996 the Polar satellite discovered a constant rain of small comets impacting the earth. Unlike large comets, whose cores are estimated to be as much as 25 mi (40 km) in diameter, these are only up to 40 ft (12 m) wide. It is estimated that as many as 43,000 reach the earth each day and break up at altitudes of 600–15,000 mi (950–24,000 km). Also in 1996 the ROSAT satellite (see X-ray astronomy) detected X-rays emanating from the Comet Hyakutake. This was completely unexpected, and can be explained by no known mechanism. Observation of more large comets passing through the solar system by orbiting X-ray observatories will be necessary to corroborate this finding.