A systematic theoretical and experimental study of Zeeman spin splittings a
nd g factors in semiconductor nanostructures is given. Six-band effective-m
ass calculations of electron, hole, and exciton spin splittings are made an
d are shown to account for experimental results presented here on In0.10Ga0
.90As/GaAs systems for the size dependences of g factors in deep-etched qua
ntum dots and wires and for the magnetic-field dependences of the Zeeman sp
littings in quantum wells. These effects are traced to band mixing, and an
analytic form of the results is given that connects these two effects and d
escribes their dependences on dimensionality.