  We review recent theoretical developments about the role of spins,
electron-electron interactions, and spin-orbit coupling in metal nanoparticles
and semiconductor quantum dots. For a closed system, in the absence of
spin-orbit coupling or of an external magnetic field, electron-electron
interactions make it possible to have ground states with spin $S > 1/2$. We
review here a theoretical analysis which makes predictions for the probability
of finding various values of spin $S$ for an irregular particle in the limit
where the number of electron is large but finite. We also present results for
the probability distribution of the spacing between successive groundstate
energies in such a particle. In a metallic particle with strong spin-orbit
interactions, for odd electron number, the groundstate has a Kramers'
degeneracy, which is split linearly by a weak applied magnetic field. The
splitting may be characterized by an effective $g$-tensor whose principal axes
and eigenvalues vary from one level to another. Recent calculations have
addressed the joint probability distribution, including the anisotropy, of the
eigenvalues. The peculiar form of the spin-orbit coupling for a two-dimensional
electron system in a GaAs heterostructure or quantum well leads to a strong
suppression of spin-orbit effects when the electrons are confined in a small
quantum dot. Spin-effects can be enhanced, however, in the presence of an
applied magnetic field parallel to the layer, which may explain recent
observations on fluctuations in the conductances through such dots. We also
discuss possible explanations for the experimental observations by Davidovic
and Tinkham of a multiplet splitting of the lowest resonance in the tunneling
conductance through a gold nano-particle.
