  BaVS3 is a moderately correlated d-electron system with a rich phase diagram.
To construct the corresponding minimal electronic model, one has to decide
which d-states are occupied, and to which extent. The ARPES experiment
presented here shows that the behavior of BaVS3 is governed by the coexistence
of wide-band (A_1g) and narrow-band (twofold degenerate E) d-electrons. We
sketch a lattice fermion model which may serve as a minimal model of BaVS3.
This serves foremost for the understanding of the metal-insulator in pure BaVS3
and its absence in some related compounds. The nature of the low temperature
magnetic order differs for several systems which may be described in terms of
the same electron model. We describe several recent experiments which give
information about magnetic order at high pressures. In particular, we discuss
field-induced insulator-to-metal transition at slightly subcritical pressures,
and an evidence for magnetic order in the high-pressure metallic phase. The
phase diagram of Sr-doped BaVS3 is also discussed. The complexity of the phases
of BaVS3 arises from the fact that it is simultaneously unstable against
several kinds of instabilities.
