Absolute concentration measurements of atoms and radicals in flames are very important for a better understanding of combustion mechanisms. Recently, several laser based methods were successfully used for such measurements. Among them are laser induced fluorescence (LIF), intracavity laser absorption spectroscopy (ICLAS) and cavity ring-down spectroscopy (CRDS). This article attempts to review and discuss the current status of the application of these techniques to the absolute concentration measurements in flames. The principles of two absorption spectroscopy methods, ICLAS and CRDS, are discussed in more detail as these methods are only at the beginning stage of their application to combustion diagnostics. The final portion of the review is devoted to discussing some recent measurements of absolute concentrations of radicals in hydrocarbon flat premixed flames and comparing these measurements with computer simulations.