This paper reviews the basics of kinetic modelling in low-temperature N 2 -O 2 plasmas, including the strong coupling between electron, vibrational, chemical and surface kinetics. The main approaches to investigate each of these kinetics are outlined and the most widely used ones are discussed in some detail. The interdependency of the different kinetics is also considered. In such a formulation, the building blocks of kinetic models in molecular plasmas are the electron Boltzmann equation, a system of rate balance equations describing the creation and loss of the most important neutral and charged heavy-particles, including the relevant vibrationally excited states and all vibration energy transfers, a proper description of transport of charged particles, and a description of heterogeneous particle destruction and molecule formation. All the details required to build a model for N 2 -O 2 plasmas are given either explicitly or by indicating relevant references, so that the interested reader has all the necessary information to build a similar model. Some new calculations are presented to illustrate and study a few specific phenomena, including the electron power transfer in air plasmas, the formation of the vibrational distribution function in O 2 dc discharges, the calculation of gas heating in pulsed air plasmas, and the heterogeneous formation of ozone in an oxygen afterglow. Finally, some open challenges and directions for further research are pointed out.