Molecules bearing a 4,4-difluoro-8-(aryl)-1,3,5,7-tetramethyl-2,6-diethyl-4-bora-3a,4a-diaza-s-indacene (bodipy) core and 1-pyrenyl-1-phenyl-4-(1-ethynylpyrene), or 1-phenyl-4-[1-ethynyl-(6-ethynylpyrene)pyrene] units were constructed in a step-by-step procedure based on palladium(0)-promoted cross-coupling reactions with the required preconstructed modules. X-ray structures of single crystals reveal a twisted arrangement of the two chromophores. In one case, an almost perfect orthogonal arrangement is found. These dyes are strongly luminescent in solution and display rich electrochemistry in which all redox processes of the bodipy and pyrene fragments are clearly resolved. The absorption spectra indicate that the bodipy and pyrene chromophores are spectrally isolated, thereby inducing a large "virtual" Stokes shift. The latter is realised by efficient transfer of intramolecular excitation energy by the Förster dipole-dipole mechanism. The rate of energy transfer depends on the structure of the dual-dye system and decreases as the centre-to-centre separation increases. The energy transfer efficiency, however, exceeds 90 % in all cases. The linkage of two pyrene residues by an ethyne group leads to a decrease in the energy-transfer efficiency, with the two polycycles acting as a single chromophore. The directly linked bodipy-pyrene dual dye binds to DNA and operates as an efficient solar concentrator when dispersed in plastic.