Climate change triggered by the excessive use of fossil fuels has resulted in an increased focus on the use of hydrogen. In addition to its clean property, hydrogen exhibits a higher efficiency for fuel cell applications compared to heat engines. Although hydrogen is one of the most common elements on Earth, it is not readily available in its elemental form in nature, indicating that it is a secondary energy source that requires the processing of hydrocarbons or water. Currently, hydrogen is predominantly produced using fossil fuels (96%), and the large-scale production of hydrogen from natural gas has already been commercialized. However, the increasing demand for on-site/distributed power generation systems has necessitated the development of a small-scale hydrogen production process. This scale-down induces a decrease in thermal efficiency and an increase in processing capacity, which compels the development of an integrated and harmonized technology. Studies are being conducted on compact reformers in this regard. The core unit processes of compact reformer include steam reforming of methane (SRM), water–gas shift (WGS), and preferential CO oxidation (PROX), with each process requiring the development of customized catalysts. This review introduces the basic thermodynamics and kinetics of these core unit processes, details their various issues, and provides a guide regarding current research trends on the development of customized catalysts for the unit processes of SRM, WGS, and PROX in compact reformers. State of the art for compact reformers are also introduced, showing that there are only several types of commercial compact reformers yet compared to their importance.