Combustion reactions quench in small volumes due to fast heat escape via the volume boundary. Nevertheless, the reaction between hydrogen and oxygen was observed in nano- and micro-bubbles. The bubbles containing a mixture of gases were produced in microsystems using electrochemical decomposition of water with a fast switching of voltage polarity. In this paper, we review our experimental results on the reaction in micro- and nano-bubbles and provide their physical interpretation. Experiments were performed using microsystems of different designs. The process was observed with a stroboscope and with a vibrometer. The latter was used to measure the gas concentration in the electrolyte and to monitor pressure in a reaction chamber covered with a flexible membrane. Information on the temperature was extracted from the Faraday current in the electrolyte. Since the direct observation of the combustion is complicated by the small size and short time scale of the events, special attention is paid to the signatures of the reaction. The mechanism of the reaction is not yet clear, but it is obvious that the process is surface dominated and happens without significant temperature increase.