This paper presents a comprehensive review of the literature on one-dimensional (1D) nanostructures (nanowires, nanoribbons, nanotubes, nanobelts, and nanofibers) of π-conjugated small molecules, oligomers, and polymers. The diverse methods used in assembling the molecular building blocks into 1D functional nanostructures and nanodevices are discussed, including hard and soft template-assisted synthesis, electrospinning, nanolithography, self-assembly in solution and at interfaces, physical vapor transport, and other strategies. Optical, charge transport, electronic, and photoconductive properties of nanowires and nanotubes of selected classes of π-conjugated molecular systems are discussed next, highlighting unique features of the 1D nanostructures compared to 2D thin films. Overview of applications of these 1D organic nanostructures ranging from nanoscale light-emitting diodes, field-emission devices, organic photovoltaics, sensors/biosensors, spin-electronics, and nanophotonics to nanoelectronics is then given. The final section provides our brief concluding comments on the status of the field and on areas of outstanding challenges and opportunities for future work. We believe that the emerging confluence of nanoscience and organic semiconductors will greatly enrich both fields while leading to enhanced performance in organic electronics and affordable nanotechnologies.