In multiple-quantum n.m.r. spectroscopy of N coupled spins one obtains n-quantum Fourier transform spectra, where n = 0, 1, 2,..., N. The spectra of particular interest are often those with high n, which may be analysable for a complex molecule without the need for isotopic spin labelling. For example, the n = N quantum spectrum is independent of dipolar couplings and gives the total chemical shift. For n = N - 1, one obtains a spectrum analogous to those from all possible singly isotopically labelled molecules (e.g. one doublet corresponding to one singly labelled species for n = 5 in orientated benzene) and for n = N - 2 all possible doubly isotopically labelled species (e.g. three triplets corresponding to three doubly labelled species for n = 4 in orientated benzene). For large n the intensity decreases, so an important question is whether selective excitation of n-quantum transitions is possible, namely, can one design pulse sequences such that only a particular n or set of n's is excited? This corresponds to the absorption of only groups of n quanta. It is shown that this can indeed be achieved by employing a combination of time-reversal sequences and phase shifts. The principles of the theory are outlined and examples of experimental results for large n in solids and liquid crystals are presented. The discussion includes spectra, statistical treatment of intensities, degree of selectivity and n-quantum relaxation. Selectivity is also possible in detection and examples of the sensitivity enhancement this provides are shown.