We study spectrally resolved dynamics of Forster energy transfer in single monolayers and bilayers of semiconductor nanocrystal quantum dots assembled using Langmuir-Blodgett (LB) techniques. For a single monolayer, we observe a distribution of transfer times from ~50 ps to ~10 ns, which can be quantitatively modeled assuming that the energy transfer is dominated by interactions of a donor nanocrystal with acceptor nanocrystals from the first three shells surrounding the donor. We also detect an effective enhancement of the absorption cross section (up to a factor of 4) for larger nanocrystals on the red side of the size distribution, which results from strong, inter-dot electrostatic coupling in the LB film (the light-harvesting antenna effect). By assembling bilayers of nanocrystals of two different sizes, we are able to improve the donor-acceptor spectral overlap for engineered transfer in a specific (vertical) direction. These bilayers show a fast, unidirectional energy flow with a time constant of ~120 ps.