Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because in secular theories the disturbing function is generally averaged over the Sun's orbital motion, whereas instead one should take into account some periodic terms, most notably the so-called ``evection'', which can be large for distant, slow-moving satellites. Here it is demonstrated that the evection and other terms from lunar theory can be incorporated into the more modern Kozai formalism, and that our synthetic approach produces much better agreement with results from symplectic integrations. Using this method, the locations of secular resonances are plotted in the orbital-element space inhabited by the irregular satellites. The present model is found to predict correctly those satellites that are resonant or near-resonant.

The octupole term in the disturbing function is also analyzed to determine the strengths of resonant-locking for satellites whose longitudes of pericenter are librating. By independently integrating these satellites' nominal orbits using a symplectic integrator, the strength of this resonance can be successfully obtained from simple analytical arguments.

To elucidate the capture of Jupiter's irregular moons, we reverse-evolve satellites from their present orbits to their original heliocentric paths in the presence of Jupiter's primordial circumplanetary disk. These orbital histories use a symplectic integrator that allows dissipation. The present satellites Himalia, Elara, Lysithea and Leda are assumed to be collisional fragments of a single parent. The simulations show that this prograde-cluster progenitor could be derived from objects with heliocentric orbits like those of the Hilda asteroid group. The capture is shown to be energetically possible using analytical approach. The spectroscopic characteristics of the prograde cluster members are compared with those of the Hildas, with the conclusion that the surface color of the prograde-cluster progenitor is consistent with an origin within the Hilda group.

The effects of radiation forces on small irregular satellites are also explored. Two new radiation effects, the orbital YORP and the gradient Yarkovsky effect are presented as possible perturbations on irregular satellites' orbits. It is found that the orbital evolution of irregular moons due to radiation effects is small, but that their rotation should be strongly dominated by YORP effect. Various spin orbit resonances are found to be likely for many small irregular satellites.

The distribution of irregular satellite clusters in the space of proper orbital elements appears to be non-random. The large majority of irregular-satellite groups cluster are found close to the secular resonances, with several objects having practically stationary pericenters. The name ``Main Sequence'' is proposed to describe this grouping, and it is noted that none of the largest satellites (those with radii $R>$ 100 km) belong to this class. Finally, this dichotomy appears to imply that the smaller near-resonant satellites might have been captured differently than the largest irregulars.