Plasma bubbles are created in an ambient discharge plasma. A bubble is a plasma volume of typically spherical shape, which is separated from the ambient plasma by a negatively biased grid of high transparency. Ions and electrons from the ambient plasma flow into the bubble volume. In steady state the flow of particles and currents is divergence-free, which is established by the plasma potential inside the bubble. The grid has two sheaths, one facing the ambient plasma, the other the bubble plasma. The inner sheath is observed to become unstable, causing the plasma potential in the bubble to oscillate. The instability arises from an excess of ions and a deficiency of electrons. Its frequency is in the range of the ion plasma frequency but depends on all parameters which influence the charge density in the sheath. When the grid voltage is very negative, electrons cannot enter the outer sheath, and the inner sheath becomes a virtual anode which reflects ions such that the bubble interior is empty. When an electron source is placed into the bubble it can neutralize the ions and the bubble refills. Without plasma sources or sinks the bubble plasma is extremely sensitive to perturbations by probes. Modified current-voltage characteristics of Langmuir and emissive probes are demonstrated. A sequence of papers first describes the basic steady-state properties, then the time evolution of bubbles, the effects of electron sources in bubbles, and the role of the grid and bubble geometry. The physics of plasma bubbles is important to several fields of basic plasma physics such as sheaths, sheath instabilities, diagnostic probes, electrostatic confinement, and current and space charge neutralization of beams. V C 2012 American Institute of Physics. [http://dx.