We present results from observations of diffuse interstellar clouds, with discussion of their significance and including a historical survey to put the recent work into perspective. A catalogue has been prepared of molecular data for diffuse clouds, putting observations by different observers onto a common basis. Although most of the spectra were not taken at the highest resolution, the results of comparing column densities for different species, as presented here, has statistical significance for chemical models and in estimating the H2 abundance. To consider molecules in individual interstellar clouds, it is essential to observe with the highest available spectroscopic resolution. We have obtained high-resolution (R.tbd;λ/Πλ= 3 à 10⁵) observations of interstellar CH, CH⁺ and CN. The formation of CH⁺ in interstellar clouds is a particular problem as relatively high temperatures (ca. 4000 K) are required to drive the most plausible production reaction, which is endothermic, and observations do not confirm the predictions of shock models. The recently installed Ultra-High-Resolution-Facility on the Anglo-Australian Telescope gives resolving powers R of order 10⁶, which is expected to result in fundamental advances in dealing with this and other outstanding problems in interstellar chemistry. Finally, we present the results of observational searches for the C60 molecule, buckminsterfullerene.