The global shift of energy production from fossil fuels to renewable energy sources requires more efficient and reliable electrochemical energy storage devices. In particular, the development of electric or hydrogen powered vehicles calls for much-higher-performance batteries, supercapacitors and fuel cells than are currently available. In this review, we present an approach to synthesize electrochemical energy storage materials to form strongly coupled hybrids (SC-hybrids) of inorganic nanomaterials and novel graphitic nano-carbon materials such as carbon nanotubes and graphene, through nucleation and growth of nanoparticles at the functional groups of oxidized graphitic nano-carbon. We show that the inorganic-nano-carbon hybrid materials represent a new approach to synthesize electrode materials with higher electrochemical performance than traditional counterparts made by simple physical mixtures of electrochemically active inorganic particles and conducting carbon materials. The inorganic-nano-carbon hybrid materials are novel due to possible chemical bonding between inorganic nanoparticles and oxidized carbon, affording enhanced charge transport and increased rate capability of electrochemical materials without sacrificing specific capacity. Nano-carbon with various degrees of oxidation provides a novel substrate for nanoparticle nucleation and growth. The interactions between inorganic precursors and oxidized-carbon substrates provide a degree of control over the morphology, size and structure of the resulting inorganic nanoparticles. This paper reviews the recent development of inorganic-nano-carbon hybrid materials for electrochemical energy storage and conversion, including the preparation and functionalization of graphene sheets and carbon nanotubes to impart oxygen containing groups and defects, and methods of synthesis of nanoparticles of various morphologies on oxidized graphene and carbon nanotubes. We then review the applications of the SC-hybrid materials for high performance lithium ion batteries, rechargeable Li-S and Li-O2 batteries, supercapacitors and ultrafast Ni-Fe batteries, and new electrocatalysts for oxygen reduction, oxygen evolution and hydrogen evolution reactions.