In this paper we report the investigation of the laser-induced breakdown and ignition behaviour of methane/air and dimethyl ether (DME)/air mixtures. Moreover, the optical emission from the induced plasma is utilized for determining the mixture composition quantitatively by means of laser-induced breakdown spectroscopy (LIBS). To the best of the authors' knowledge, LIBS and laser ignition of DME have not been reported in literature before. The technique under investigation is finally employed for combustion diagnostics in laminar as well as turbulent flames. In the laminar premixed and non-premixed flames the LIBS spectra allow spatially resolved measurements of the equivalence ratio and enable studying the mixing of gases provided through the burner with the surrounding room air. In addition, the breakdown threshold of the applied laser pulse energy yields an estimate for the local temperature. In the turbulent cases single-shot LIBS spectra are recorded at fixed position allowing the derivation of local statistical fluctuations of the equivalence ratio in partially premixed jet flames. The results show that laser-induced breakdowns have a strong potential for flame diagnostics and, under suitable conditions, for the ignition of combustible mixtures.