Around the world, there is a growing interest in integrated STEM (science, technology, engineering, mathematics) education. Many of the calls for integrated STEM emphasize the need for students to engage with complex STEM problems that cut across multiple fields. Yet there is a need to clarify the nature of those problems and differentiate STEM problems from those of different kinds. This conceptual work examines the nature of STEM problems in order to inform pre-college educational efforts in STEM. A typology is introduced that situates STEM problems within a broader space of problems within STEM and non-STEM fields, and the characteristics of STEM problems are described. The typology and characteristics are then applied to different approaches to STEM instruction. A key conclusion is that many integrated STEM education efforts tend to focus on STEM problems that are narrowly framed and that do not include attention to social, cultural, political, or ethical dimensions. However, alternative instructional approaches exist that re-introduce those missing dimensions. If STEM education is to prepare students to grapple with complex problems in the real world, then more attention ought to be given to approaches that are inclusive of the non-STEM dimensions that exist in those problems.