The interplay of electron correlations and impurities in one-dimensional electron systems leads to striking effects in the low energy physics. The conductance in addition depends strongly on the properties of the contacts (``adiabatic'' versus ``abrupt''). Results for the conductance using a functional renormalization group (fRG) approach which is perturbative in the two-body interaction, but non-perturbative in the impurity strength are presented. The comparison with exact numerical results for small chain length shows that the truncated fRG is surprisingly accurate even for moderate interaction strength (cond-mat/0304517). After presenting fRG results for the scaling function in the case of a single impurity the resonant tunneling through a double barrier is discussed. Calculations of the peak conductance G_p(T) as a function of temperature T over several decades show parameter regimes with distinctive power law behaviour. For intermediate dot parameters and T of the order of the level spacing of the dot, G_p(T) is shown to decrease for decreasing T in a non-universal way. No regime of ``correlated sequential tunneling'' is found (cond-mat/0304655). Abrupt contacts and more complicated geometries, like ``Y-junctions'' are discussed shortly.