This paper reviews methods which can be used to detect binaries involving low-and intermediate-mass stars, with special emphasis on evolved systems. Besides the traditional methods involving radial-velocity or photometric monitoring, the paper discusses as well less known methods involving astrometry or maser (non-)detection. An extensive list of internet resources (mostly catalogues/databases of orbits and individual measurements) for the study of binary stars is provided at the end of the paper. FIGURE 2. The various kinds of symbiotic stars (SyS) and of peculiar red giants, in a plane spectraltype vs. metallicity. Within each box, the first line (slanted font) lists the stellar family, the second line (calligraphic font) indicates whether or not stars from that family are enriched in s-process elements (either from internal nucleosynthesis -"Intrinsic Ba" -or from mass transfer across a binary system -"Ba" standing for Extrinsic Ba). The last lines (regular font) provide the binary properties of that family: binary (short or long periods) or non-binary, SyS or non-SyS. Each box has been assigned a number, for easy reference in the text. The horizontal line with an arrow in the middle of the figure is to indicate that the thermally-pulsing AGB phase (where the s-process nucleosynthesis takes place) involves different spectral types at low-and near-solar metallicity. (From [5]) synthesis, being more efficient at low metallicities [19], and (iii) the location of evolutionary tracks in the Hertzsprung-Russell diagram (hence the correspondence between spectral type and evolutionary status, like the onset of thermally-pulsing AGB, where the s-process operates, will depend on metallicity). Fig. 2 therefore considers three different metallicity ranges: (i) [Fe/H]< −1, corresponding to the halo population; (ii) −1 ≤[Fe/H]≤ 0, or disk metallicity; (iii) [Fe/H]≥ 0, solar and super-solar metallicities found in the young thin disk.The horizontal axis in Fig. 2 displays spectral type. At a given metallicity, spectral type is a proxy for evolutionary status: the giant components in L&IM binaries may either be located on the first red giant branch (RGB), in the core He-burning phase (which is hardly distinguishable from the lower RGB/AGB; CH giants probably belong to that phase), He-shell burning early AGB (E-AGB), or on the thermally-pulsing AGB (TP-AGB) phase, where the s-process operates.Symbiotic activity is expected in the middle of this spectral sequence, because (i) at the left end, stars (like CH) are not luminous enough to experience a mass loss sufficient to power symbiotic activity; (ii) at the right end, the stars with the barium syndrome need not be binaries. Indeed, in TP-AGB stars, heavy-elements are synthesized in the stellar interior and dredged-up to the surface, so that "intrinsic Ba" (or S) stars occupy the rightmost boxes -4 and 8 -of Fig. 2, and hence need not exhibit any symbiotic activity since they are single stars (For examples of stars belonging to box 4, see [18] and [20]). Such evolved giants whic...