  We propose a formalism which uses boundary conditions imposed on the
Luttinger liquid (LL) to describe the transport properties of a LL coupled to
reservoirs. The various boundary conditions completely determine linear
transport in the joint system reservoirs+LL. As an illustration we consider an
exactly solvable microscopic model in a multi-terminal geometry for which such
boundary conditions can be explicitly derived; in this model the
Landauer-B\"uttiker formalism fails: if it were valid, the relation between the
conductance matrix elements and the reflection and transmission coefficients
could yield negative probabilities. We then apply our formalism to a discussion
of shot noise through an impurity in a LL connected to two reservoirs.
