Future Internet technologies will be affected not only by limited bandwidth of information infrastructure, but also by its energy consumption. In order to solve both problems simultaneously, in this invited paper, we describe several energy-efficient (EE) hybrid coded-modulation (CM) schemes enabling Terabit optical Ethernet: EE 4D CM, EE generalized- OFDM, and EE spatial-domain-based CM. A common property of these is employment of EE modulations, various degrees of freedom and rate-adaptive coding. These EE schemes are called hybrid as all available degrees of freedom are used for transmission over optical fibers including amplitude, phase, polarization and OAM. Since the channel capacity is a linear function in number of dimensions, by increasing the number of basis functions, we can dramatically improve overall capacity. The EE problem is solved by properly designing multi-dimensional signal constellations such that transinformation is maximized, while taking the energy constraint into account.