Each of our giant planets has a regular and an irregular system
of moons.  Regular moons lie very close to the planet’s equatorial
plane on nearly-circular direct orbits that share the planetary
rotational sense, and likely formed in the disk.  Irregular moons,
in contrast, orbit at nearly all orbital inclinations (including
retrograde) and often have very eccentric orbits; these properties
alone lead one to believe that the regular moons were born in an
accretion disk around each forming planet while the irregulars
(or ancient precursors) were captured into orbit around the planet.
I will review observational techniques by which we discover these
moons, the current observational inventory and limits, what is
suspected about the origin and evolution of the irregular
moon systems we see today, and future prospects for learning more.