The core microbiome, which refers to a set of consistent microbial features across populations, is of major interest in microbiome research and has been addressed by numerous studies. Understanding the core microbiome can help identify elements that lead to dysbiosis, and lead to treatments for microbiome-related health states. However, defining the core microbiome is a complex task at several levels. In this review, we consider the current state of core human microbiome research. We consider the knowledge that has been gained, the factors limiting our ability to achieve a reliable description of the core human microbiome, and the fields most likely to improve that ability. DNA sequencing technologies and the methods for analyzing metagenomics and amplicon data will most likely facilitate higher accuracy and resolution in describing the microbiome. However, more effort should be invested in characterizing the microbiome's interactions with its human host, including the immune system and nutrition. Other components of this holobiontic system should also be emphasized, such as fungi, protists, lower eukaryotes, viruses, and phages. Most importantly, a collaborative effort of experts in microbiology, nutrition, immunology, medicine, systems biology, bioinformatics, and machine learning is probably required to identify the traits of the core human microbiome.