Low-rank coals, biomass, and heavy petroleum are typical heavy carbon resources, which are currently not efficiently used, and many processes for the current use of the heavy carbon resources cause severe environmental pollution with very limited economic benefits even with a great deficit. Efficiently using the heavy carbon resources can greatly improve the environment and create huge economic benefits. The main difficulty in efficiently using the heavy carbon resources is the high content of aromatic rings (ARs) and heteroatoms in addition to the insoluble and complex macromolecular structures of the heavy carbon resources. Catalytic hydroconversion (CHC) includes catalytic hydrocracking and subsequent catalytic hydrofining. Many low-rank coals consist of macromolecular species, which are rich in bridged linkages connecting structural units, especially ARs, on which side chains are usually contained. Many ARs, bridged linkages, and side chains contain heteroatoms. Over a proper active catalyst, many bridged linkages and even some side chains can be cleaved, and many heteroatoms outside the ARs can be removed by the CHC under mild conditions to get soluble portions with relatively simple composition, facilitating subsequent separation to obtain pure chemicals, especially value-added products, such as condensed aromatics. The remaining economically inseparable species can be converted to liquid chemicals, especially nonsubstituted and alkyl-substituted cyclanes, by subsequent catalytic hydrofining. Catalysts and catalytically formed active hydrogen play crucial roles in the processes. Mainly based on our investigations, the related advances are reviewed in this work.