Newly developed techniques for producing beams of superfluid helium nanodroplets and for embedding single molecules or unstable particles (clusters and radicals) in such droplets make it possible to study the spectra of molecules and clusters in a new type of gentle quantum matrix — liquid superfluid helium. This paper reviews research into the spectroscopy of single molecules and clusters inside helium nanodroplets. Methods used in producing and studying helium nanodroplets in molecular beams formed during gas outflow from a cooled expansion nozzle are described, as are methods for embedding single molecules and clusters into droplets and spectroscopy techniques for single molecules and clusters inside helium nanodroplets. It is shown that the properties of helium nanodroplets themselves can be studied by performing spectroscopic measurements. Experiments on the synthesis of aligned molecular chains and those on the observation of chemical reactions inside helium nanodroplets are considered. Several properties of helium nanodroplets and trapped Bose-Einstein condensates are compared. The potential of the method and some unsolved problems are also discussed.