Due to their quasi-one-dimensional structure, the conductance of
quantum wires is expected to be quantized in units of the conductance
quantum G_0=2e^2/h. However, a number of recent experiments report
deviations from perfect conductance quantization, such as the
so-called 0.7-anomaly observed below the first plateau. These
experiments have stimulated much theoretical interest in the physics
of one-dimensional conductors not captured by the Luttinger-liquid
theory. The talk concentrates on the transition from a one-dimensional
to a quasi-one-dimensional state. In the absence of interactions
between electrons, this corresponds to filling up the second subband
of transverse quantization. On the other hand, strongly interacting
one-dimensional electrons form a Wigner crystal, and the transition
corresponds to it splitting into two chains (zigzag crystal). The
evolution of the system and the electronic excitation modes in the
vicinity of the transition are studied as the interaction strength
changes. Furthermore, the spin properties in the Wigner crystal regime
are addressed. While the spin properties of the one-dimensional
crystal are relatively simple, we find several interesting spin
structures in the zigzag crystal.