Epigenomic mapping of tissue samples generates critical insights into genome-wide regulations of gene activities and expressions during normal development and disease processes. Epigenomic profiling using a low number of cells produced by patient and mouse samples presents new challenges to biotechnologists. In this review, we first discuss the rationale and premise behind profiling epigenomes for precision medicine. We then examine the existing literature on applying microfluidics to facilitate low-input and high-throughput epigenomic profiling, with emphasis on technologies enabling interfacing with next-generation sequencing. We detail assays on studies of histone modifications, DNA methylation, 3D chromatin structures and non-coding RNAs. Finally, we discuss what the future may hold in terms of method development and translational potential.