Extensive theoretical and experimental studies have been carried out f
or the past 20 years on electron-ion recombination processes, as they
are applied to the analysis of astrophysical and laboratory plasmas. W
e review the basic understanding gained through these efforts, with em
phasis on some of the more recent progress made in recombination theor
y as the recombining system is affected by time-dependent electric fie
lds and plasma particles at low temperature. Together with collisional
ionization and excitation processes, recombination is important in de
termining ionization balance and excited-state population in non-equil
ibrium plasmas. The radiation emitted by plasmas is usually the princi
pal medium with which to study the plasma condition, as it is produced
mainly during the recombination and decay of excited states of ions i
nside the plasma. This is especially true when the plasma under study
is not readily accessible by direct probes, as in astrophysical plasma
s. Moreover, external probes may sometimes cause undesirable disturban
ces of the plasma. Electron-ion recombination proceeds in several diff
erent modes. The direct modes include three-body recombination (TBR) a
nd one-step radiative recombination (RR), all to the ground- and singl
y-excited states of the target ions. By contrast, the indirect resonan
t mode is a two-step dielectronic recombination (DR), which proceeds f
irst with the formation of doubly-excited states by radiationless exci
tation/capture. The resonant states thus formed may relax by autoioniz
ation and/or radiative cascades. For more exotic modes of recombinatio
n, we consider off-shell dielectronic recombination (radiative DR = RD
R), in which an electron capture is accompanied by simultaneous radiat
ive emission and excitation of the target ion. Some discussion on atta
chment of electrons to neutral atoms, resulting in the formation of ne
gative ions, is also given. When resonance states involve one or more
electrons in high Rydberg states, presence of an external or intrinsic
electric field in the vicinity of the target ions can seriously affec
t the ionic states involved and the resulting reaction rates. Such per
turbative fields can be intrinsic, as in the case of the plasma ion fi
eld, or externally imposed. A proper theoretical treatment of this dif
ficult problem is crucial in understanding the recombination process w
hich takes place in a field contaminated environment. The simple off-s
hell dressing procedure of high Rydberg states by a time-dependent fie
ld is reviewed, and the possibility of an anomalously large enhancemen
t in the rates, due to the momentum coherence effect (MCE), is discuss
ed. The presently available data on recombination rates are summarized
, and several important deficiencies and future directions for further
research are pointed out. Based on the detailed calculations for a nu
mber of cases, several empirical rate formulae for RR and DR processes
have been generated to summarize the data for ready applications. As
the collection of atoms is cooled to very low temperatures, T < 1 mK s
imilar or equal to 10(-8) Ryd, and the bound electrons are ionized by
laser irradiation to states of very precisely controlled energies, the
prospect for accurate experimental measurements of very-low-energy re
combination rates is considered, where the electron temperature can be
very low. Therefore, it is of interest to reconsider theoretically so
me new phenomena which may occur at such cold environments, in which t
he electron de Broglie wavelength can be very large, and both the dens
ity and coherent effects, as well as possible field effects, must be p
roperly taken into account. Finally, a broader understanding of the va
rious recombination processes may be achieved by studying their relati
onships to other reactions initiated by electron, ion and photon impac
t.