Contrails (condensation trails) form behind aircraft as line-shaped cirrus clouds, with high concentrations of small ice particles compared to other cirrus (see Fig. 3-1). Contrails may form as “exhaust contrails” from water and particles emitted by the aircraft engines (Schumann 1996) or as “aerodynamic contrails” forming because of adiabatic cooling near curved surfaces of the aircraft (Gierens et al. 2009; Kärcher et al. 2009). Distrails (dissipation trails) and aircraft-induced cloud holes may also form (Heymsfield et al. 2011). Contrails are mostly short-lived but may persist for many hours when forming in ice-supersaturated air (Minnis et al. 1998). Individual contrails deform with time, often merge with other contrails and cirrus, and eventually form “contrail cirrus” (Schumann 2002). Contrail cirrus can be distinguished from other cirrus only when traced back to the formation process (Graf et al. 2012). Early studies discussed the visibility and detection aspects of contrails (aufm Kampe 1943; Brewer 1946; Appleman 1953; Ryan et al. 2011), and these studies contributed to the detection of ice supersaturation, contrail persistence, the dryness of the stratosphere, the Brewer–Dobson circulation (Brewer 2000), and hollow ice particles (Weickmann 1945). The climate impact got more attention later (Penner et al. 1999). The mean radiative forcing (RF) from contrails is likely positive, possibly contributing to global warming (Boucher et al. 2013). In contrast to many other climate effects discussed for aviation, contrail cirrus is observable (see Fig. 3-1f). This review summarizes the present understanding of contrail cirrus and identifies some open questions. The insight gained may be of relevance for cirrus research, contrail climate assessment, and mitigation (including optimized aircraft and engines, changed routing, and alternative fuels), not discussed here (Fuglestvedt et al. 2010; Lee et al. 2010; Grewe et al. 2014a; Brasseur et al. 2016). The paper describes first the formation and properties of “individual contrails.” This term is used instead of “line-shaped contrails” because it is not clear when a line-shaped contrail ends. The second part describes contrail cirrus.