The irregular moons of the Jovian planets are a puzzling part of the solar system inventory. Unlike regular satellites, the irregular moons revolve around planets at large distances in tilted and eccentric orbits. Their origin, which is intimately linked with the origin of the planets themselves, is yet to be explained. Here we report a study of the orbital and collisional evolution of the irregular satellites from times after their formation to the present epoch. The purpose of this study is to find out the features of the observed irregular moons that can be attributed to this evolution and separate them from signatures of the formation process. We numerically integrated ~60,000 test satellite orbits to map orbital locations that are stable on long time intervals. We found that the orbits highly inclined to the ecliptic are unstable due to the effect of the Kozai resonance, which radially stretches them so that satellites either escape from the Hill sphere, collide with massive inner moons, or impact the parent planet. We also found that prograde satellite orbits with large semimajor axes are unstable due to the effect of the evection resonance, which locks the orbit's apocenter to the apparent motion of the Sun around the parent planet. In such a resonance, the effect of solar tides on a resonant moon accumulates at each apocenter passage of the moon, which causes a radially outward drift of its orbital apocenter; once close to the Hill sphere, the moon escapes. By contrast, retrograde moons with large orbital semimajor axes are long-lived. We have developed an analytic model of the distant satellite orbits and used it to explain the results of our numerical experiments. In particular, we analytically studied the effect of the Kozai resonance. We numerically integrated the orbits of the 50 irregular moons (known by 2002 August 16) for 108 yr. All orbits were stable on this time interval and did not show any macroscopic variations that would indicate instabilities operating on longer time spans. The average orbits calculated from this experiment were then used to probe the collisional evolution of the irregular satellite systems. We found that (1) the large irregular moons must have collisionally eliminated many small irregular moons, thus shaping their population to the currently observed structures; (2) some dynamical families of satellites could have been formed by catastrophic collisions among the irregular moons; and (3) Phoebe's surface must have been heavily cratered by impacts from an extinct population of Saturnian irregular moons, much larger than the present one. We therefore suggest that the Cassini imaging of Phoebe in 2004 can be used to determine the primordial population of small irregular moons of Saturn. In such a case, we will also better understand the overall efficiency of the formation process of the irregular satellites and the physical conditions that existed during planetary formation. We discovered two dynamical families of tightly clustered orbits within the Jovian retrograde group. We believe that these two clusters may be the remnants of two collisionally disrupted bodies. We found that the entire Jovian retrograde group and the Saturnian inclination groups were not produced by single breakups, because the ejection velocities derived from the orbital structures of these groups greatly exceed values calculated by modern numerical models of collisional breakups. Taken together, the evidence presented here suggests that many properties of the irregular moons previously assigned to their formation process may have resulted from their later dynamical and collisional evolution. Finally, we have found that several irregular moons, namely, Pasiphae, Sinope, S/2001 J10, S/2000 S5, S/2000 S6, and S/2000 S3, have orbits characterized by secular resonances. The orbits of some of these moons apparently evolved by some slow dissipative process in the past and became captured in tiny resonant volumes.