Direct conversion of methane to methanol is an effective and practical process to improve the efficiency of natural gas utilization. Copper (Cu)-based catalysts have attracted great research attention, due to their unique ability to selectively catalyze the partial oxidation of methane to methanol at relatively low temperatures. In recent decades, many different catalysts have been studied to achieve a high conversion of methane to methanol, including the Cu-based enzymes, Cu-zeolites, Cu-MOFs (metal-organic frameworks) and Cu-oxides. In this mini review, we will detail the obtained evidence on the exact state of the active Cu sites on these various catalysts, which have arisen from the most recently developed techniques and the results of DFT calculations. We aim to establish the structure-performance relationship in terms of the properties of these materials and their catalytic functionalities, and also discuss the unresolved questions in the direct conversion of methane to methanol reactions. Finally, we hope to offer some suggestions and strategies for guiding the practical applications regarding the catalyst design and engineering for a high methanol yield in the methane oxidation reaction.