We discuss how Coulomb explosion imaging (CEI), triggered by intense femtosecond laser pulses and combined with laser-induced alignment and covariance analysis of the angular distributions of the recoiling fragment ions, provides new opportunities for imaging the structures of molecules and molecular complexes. First, focusing on gas phase molecules, we show how the periodic torsional motion of halogenated biphenyl molecules can be measured in real time by timed CEI, and how CEI of one-dimensionally aligned difluoroiodobenzene molecules can uniquely identify four structural isomers. Next, focusing on molecular complexes formed inside He nano-droplets, we show that the conformations of noncovalently bound dimers or trimers, aligned in one or three dimensions, can be determined by CEI. Results presented for homodimers of CS2, OCS, and bromobenzene pave the way for femtosecond time-resolved structure imaging of molecules undergoing bimolecular interactions and ultimately chemical reactions.