The study of layered materials has been a significant and fascinating area due to their unique physical and chemical properties. Among various layered materials, lanthanum copper oxychalcogenides (LaCuOX (X=S, Se, Te)) have drawn a lot of attention of researchers. The study of LaCuOX was initially focused on the optoelectronic performance due to its excellent optical and electronic properties. Recently, it was found that the layered LaCuOX material also exhibits good thermoelectric properties, providing an opportunity to achieve high energy conversion efficiency through the thermoelectric effects. In this report, an overview of recent advances in LaCuOX research is provided, including crystal and electronic structure, synthetic methods, physical properties, practical applications as well as some strategies to optimize their transport properties. Theoretical and experimental results on LaCuOX crystals or thin films are both discussed in this report. Finally, the challenges and outlook for LaCuOX are evaluated based on current progress.