A Penning trap is a device for the storage of charged particles using a homogeneous magnetic field and a quadrupole electric field. It is mostly found in the physical sciences and related fields of study for precision measurements of properties of ions and stable subatomic particles, like for example mass, fission yields and isomeric yield ratios. One initial object of study was the so-called geonium atoms, which represent a way to measure the electron magnetic moment by storing a single electron. These traps have been used in the physical realization of quantum computation and quantum information processing by trapping qubits. Penning traps are in use in many laboratories worldwide, including CERN, to store and investigate anti-particles such as antiprotons. The main advantages of Penning traps are the potentially long storage times and the existence of a multitude of techniques to manipulate and non-destructively detect the stored particles. This makes Penning traps versatile for the investigation of stored particles, but also for their selection, preparation or mere storage.

The Penning trap was named after F. M. Penning (1894–1953) by Hans Georg Dehmelt (1922–2017) who built the first trap. Dehmelt got inspiration from the vacuum gauge built by F. M. Penning where a current through a discharge tube in a magnetic field is proportional to the pressure. Citing from H. Dehmelt's autobiography:

"I began to focus on the magnetron/Penning discharge geometry, which, in the Penning ion gauge, had caught my interest already at Göttingen and at Duke. In their 1955 cyclotron resonance work on photoelectrons in vacuum Franken and Liebes had reported undesirable frequency shifts caused by accidental electron trapping. Their analysis made me realize that in a pure electric quadrupole field the shift would not depend on the location of the electron in the trap. This is an important advantage over many other traps that I decided to exploit. A magnetron trap of this type had been briefly discussed in J.R. Pierce's 1949 book, and I developed a simple description of the axial, magnetron, and cyclotron motions of an electron in it. With the help of the expert glassblower of the Department, Jake Jonson, I built my first high vacuum magnetron trap in 1959 and was soon able to trap electrons for about 10 sec and to detect axial, magnetron and cyclotron resonances." – H. Dehmelt

H. Dehmelt shared the Nobel Prize in Physics in 1989 for the development of the ion trap technique.

Penning traps use a strong homogeneous axial magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially. The static electric potential can be generated using a set of three electrodes: a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive (negative) ions, the endcap electrodes are kept at a positive (negative) potential relative to the ring. This potential produces a saddle point in the centre of the trap, which traps ions along the axial direction. The electric field causes ions to oscillate (harmonically in the case of an ideal Penning trap) along the trap axis. The magnetic field in combination with the electric field causes charged particles to move in the radial plane with a motion which traces out an epitrochoid.

The orbital motion of ions in the radial plane is composed of two modes at frequencies which are called the magnetron ${\displaystyle \omega _{-}}$and the modified cyclotron ${\displaystyle \omega _{+}}$ frequencies. These motions are similar to the deferent and epicycle, respectively, of the Ptolemaic model of the solar system.

The sum of these two frequencies is the cyclotron frequency, which depends only on the ratio of electric charge to mass and on the strength of the magnetic field. This frequency can be measured very accurately and can be used to measure the masses of charged particles. Many of the highest-precision mass measurements (masses of the electron, proton, ²H, ²⁰Ne and ²⁸Si) come from Penning traps.

Buffer gas cooling, resistive cooling, and laser cooling are techniques to remove energy from ions in a Penning trap. Buffer gas cooling relies on collisions between the ions and neutral gas molecules that bring the ion energy closer to the energy of the gas molecules. In resistive cooling, moving image charges in the electrodes are made to do work through an external resistor, effectively removing energy from the ions. Laser cooling can be used to remove energy from some kinds of ions in Penning traps. This technique requires ions with an appropriate electronic structure. Radiative cooling is the process by which the ions lose energy by creating electromagnetic waves by virtue of their acceleration in the magnetic field. This process dominates the cooling of electrons in Penning traps, but is very small and usually negligible for heavier particles.