In order to achieve multi-gigabit transmission (projected for 2020) for the use in interplanetary communications, the usage of large number of time slots in pulse-position modulation (PPM), typically used in deep-space applications, is needed, which imposes stringent requirements on system design and implementation. As an alternative satisfying high-bandwidth demands of future interplanetary communications, while keeping the system cost and power consumption reasonably low, in this invited paper, we describe the use of orbital angular momentum (OAM) as an additional degree of freedom. The OAM is associated with azimuthal phase of the complex electric field. Because OAM eigenstates are orthogonal the can be used as basis functions for multidimensional signaling. The OAM modulation and multiplexing can, therefore, be used, in combination with other degrees of freedom, to solve the high-bandwidth requirements of future deep-space and near-Earth optical communications. The main challenge for OAM deep-space communication represents the link between a spacecraft probe and the Earth station because in the presence of atmospheric turbulence the orthogonality between OAM states is not longer preserved. We will show that in combination with LDPC codes, the OAM-based modulation schemes can operate even under strong atmospheric turbulence regime.