Biomass contains up to 14 essential elements that serve as nutrients for plant growth and development, including photosynthesis and enzyme functionalities. These elements in different chemical forms (e.g., minerals) constitute the inorganic fraction of biomass and can cause operational issues in thermal and biochemical biomass conversion technologies. In biomass gasification and pyrolysis processes, for instance, inorganics can cause fouling, tar formation, and corrosion. In catalytic and biochemical processes, inorganics can poison catalysts, alter biochemical pathways, and modify product yields and selectivity. This review provides an overview of the inorganic content in biomass feedstocks, the critical role inorganics play in plant biochemistry, the effect that inorganics have in various thermochemical and biochemical biomass conversion technologies, and different approaches to remove them from biomass. We provide recommendations for future research, focusing on developing technologies to effectively remove inorganics from biomass, using the inorganics to improve soil quality and for alternative applications, and designing biorefineries to convert demineralized biomass obtained from diverse sources.