The results of long-term studies on the physical-mechanical properties of C60 and C70 molecular crystals (fullerites) were systematized and described. These materials are the new allotropic form of carbon in which fullerenes (stable molecules consisting of 60 and 70 atoms) represent the elementary base units. Molecules are combined into crystalline structures mainly by dispersive (van der Waals) forces with a small contribution from covalent bonds. The anomalies of the fullerite crystal structures and features of the phase transitions occurring in them, which are caused by dispersive forces, orientation ordering, and dynamics of the molecules’ rotational degrees of freedom, were discussed. The most interesting transformations of fullerite lattice structures and orientation states were observed in the temperature range of 77 K ≲ Т ≲ 350 K. The majority of the experimental investigations were carried out at these temperatures. The experiments were concentrated on the effects that lattice-orientation phase transitions had on the mechanical properties of single crystals, polycrystalline solids, and compacts. Acoustical spectroscopy at low and high oscillation frequencies, micro- and nanoindentation and macrodeformation methods were used in the experimental research. The crystallogeometric aspects and dislocation mechanisms of plastic slip in fullerites, as well as the methods of observing dislocations and studying their mobility, are described in detail. Also the influence of different external factors, namely, illumination (photoplastic effect), pulsed magnetic field (magnetoplastic effect), and sample compaction pressure (baropolymerization effect) are discussed. The effects of saturating samples of different morphology with hydrogen, oxygen, and inert gas impurities on the fullerites’ mechanical properties were considered. The discussion of the experimental results is accompanied by a brief description of their theoretical interpretation based on analyzing the interaction of elastic and plastic deformations of the fullerite lattice with the processes of orientational ordering, rotation, and librational vibrations of molecules.