The ability to upconvert two low energy photons into one high energy photon has potential applications in solar energy, biological imaging, and data storage. In this Letter, CdSe and PbSe semiconductor nanocrystals are combined with molecular emitters (diphenylanthracene and rubrene) to upconvert photons in both the visible and the near-infrared spectral regions. Absorption of low energy photons by the nanocrystals is followed by energy transfer to the molecular triplet states, which then undergo triplet-triplet annihilation to create high energy singlet states that emit upconverted light. By using conjugated organic ligands on the CdSe nanocrystals to form an energy cascade, the upconversion process could be enhanced by up to 3 orders of magnitude. The use of different combinations of nanocrystals and emitters shows that this platform has great flexibility in the choice of both excitation and emission wavelengths.