Experimental and theoretical results concerning partial discharges in liquids are presented. Experiments on the initiation of partial discharges in floating up bubbles under low background radiation were performed. An additional source of ionizing radiation (X-rays) should be used for the inception of partial discharges under these conditions. Different dynamics of floating up bubbles after partial discharges were recorded and described. In particular, the inception and development of the streamer in transformer oil from the bubble surface was observed that led to the breakdown of the electrode gap in some cases. The influence of partial discharge in one bubble (or in a glass microsphere) on the discharge inception in a neighbor bubble was studied. The experimental measurements and theoretical calculations of optical and electrical characteristics of partial discharges in the bubbles were made. The formation of partial discharge in a microbubble after the cavitation in the extremely high electric field was proved with the analysis and numerical simulation of Kerr fringes. The systematic calculations of “true” and “apparent” charges were performed for round and deformed bubbles. The theoretical dependencies obtained are in good agreement with the experimental measurements performed.