This tutorial is intended to provide a basic overview of non-equilibrium phenomena for thermal plasmas. Thermal plasmas (TPs) mainly issued from electrical discharges are often assumed to be in ≪ equilibrium ≫ as opposed to ≪ non-equilibrium plasmas ≫ where non-equilibrium phenomena are more pronounced. As a first approximation it can be shown that TPs are close to a local thermodynamic equilibrium (LTE) which is often taken as their reference state. However, in many situations, deviations from LTE can clearly exist. The main goal of this brief tutorial is to explain to interested scientists the main phenomena, mechanisms and characteristics associated to TPs or quasi-TPs. Then we introduce the different laws of the thermodynamic equilibrium applied to these plasmas and show that not all of them are valid in TPs, which lead us to define the LTE. However, even if the transport phenomena are non-equilibrium mechanisms, we show with illustrations that they are studied and estimated within the framework of the LTE. The next sections focus on phenomena named ‘departures from equilibrium’ for thermal plasmas. For convenience and educational reasons, we split them into the departures from the chemical and the thermal equilibria respectively. In each case we present and clearly define the mechanisms that promote equilibrium and those that tend to create departures. We present not only experimental setups that highlight these deviations but also the basis for the mathematical models that allow them to be simulated, before concluding the tutorial with the outlooks and challenges currently under research.