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.