The benefits of placing ultraviolet (UV) spectrographs in space were first pointed out by Spitzer (1946) and Spitzer & Zabriskie (1959), with much of the emphasis on absorption-line measurements of interstellar atoms and molecules. The first UV observations of the diffuse interstellar medium took place in the early 1970s, using sounding rockets, which were followed by a series of orbital instruments starting in the later 1970s and extending almost to the present time. Many of these observations have provided information on the chemistry of the diffuse ISM, and will be emphasized here. The most abundant molecule in space, H$_2$, is not readily observed in other wavelength bands and was first detected by a UV sounding rocket experiment (Carruthers 1970). Thereafter a series of orbital instruments, starting with the Copernicus satellite in 1972 and culminating with the launch of FUSE in 1999, carried out broad surveys of molecular hydrogen in a variety of ISM environments (e.g., Spitzer et al. 1973; Snow et al. 2000; Shull et al. 2000; see also the review by Shull & Beckwith 1982). The UV observations of electronic transitions of H$_2$, including lines arising from excited rotational levels of the ground state, have provided a wealth of information on not only the chemistry of the diffuse ISM, but also the composition and physical conditions. The second most abundant molecule in the diffuse ISM, CO, also has numerous electronic transitions in the UV, and has been widely observed by many different instruments, most usefully the Hubble Space Telescope (HST) (e.g., Lambert et al. 1994; Sheffer et al. 2002). Valuable information on diffuse ISM chemistry, isotopic composition, and physical conditions has been provided by these observations. A few additional molecules, all of them diatomics such as OH and N$_2$, have been detected through UV absorption-line observations, and many others have been sought unsuccessfully. The Cosmic Origins Spectrograph, expected to be installed aboard the HST in 2007, will have enhanced UV sensitivity and will provide information on molecular abundances in denser clouds than previously studied. One of the high priorities will be the search for electronic transitions of complex organic molecules such as PAHs.