Display omitted •The concept of a “proteome folding problem” is discussed–with the complexities of misfolded states that exist on a folding energy landscape and the cellular machinery that contends with them.•A brief discussion is offered of the physiological pressures for folding to occur such that functional, folded proteins are maintained in adequate amounts for life.•The importance of proteostasis networks for folding to occur in vivo is described.•Examples are given of computational modeling of folding in the presence of proteostasis components. Stunning advances have been achieved in addressing the protein folding problem, providing deeper understanding of the mechanisms by which proteins navigate energy landscapes to reach their native states and enabling powerful algorithms to connect sequence to structure. However, the realities of the in vivo protein folding problem remain a challenge to reckon with. Here, we discuss the concept of the “proteome folding problem”—the problem of how organisms build and maintain a functional proteome—by admitting that folding energy landscapes are characterized by many misfolded states and that cells must deploy a network of chaperones and degradation enzymes to minimize deleterious impacts of these off-pathway species. The resulting proteostasis network is an inextricable part of in vivo protein folding and must be understood in detail if we are to solve the proteome folding problem. We discuss how the development of computational models for the proteostasis network’s actions and the relationship to the biophysical properties of the proteome has begun to offer new insights and capabilities.