Diagnostic methods for the determination of absolute number densities of highly reactive free radicals in nonthermal atmospheric pressure (AP) plasmas are summarized. Broadband and laser absorption spectroscopy, single- and two-photon absorption laser-induced fluorescence spectroscopy, and molecular beam threshold ionization mass spectrometry (MS) are introduced as methods, which can reach ground states of measured species and are, therefore, able to provide quantitative information about their number densities. The advantage of optical methods is their noninvasive nature with possibility to generate 2-D or 3-D maps of species densities even in the core of the plasma and with high temporal resolution. However, the calibration procedure can be challenging, especially when fast nonradiative quenching of the excited states in fluorescence spectroscopies takes place. As a nonoptical alternative method, the MS can be applied. This diagnostic is not limited by the necessity of existence of reachable optical transition; it can be, however, applied only to the edge of the plasma and it has generally worth detection limit than the optical methods. The main features and challenges, connected with these diagnostic methods under AP conditions, are briefly discussed and references to literature are provided.