The use of design methods for innovation in business models has gained popularity recently. Despite interest in the business sector, there are still gaps in literature research on their potential to aid business applications and challenges. To understand how design methods enhance business model innovation, this study examines design research on business model innovation. We review researchers' work on design thinking for business model innovation, identifying five research themes: technological differentiation, innovation adoption in business, transforming ideas into innovative concepts, evaluating design's influence on new strategies, and assessing the role of designers in driving business innovation. We also investigate factors impacting design methods' effectiveness, such as organizational culture, resources, capabilities, industry dynamics, competition, and regulations. In conclusion, we emphasize considering design research's social and situational nature to apply it to the co-evolution of tech products, services, and models. This literature review provides a valuable resource for future researchers and practitioners interested in using these concepts in business innovation, regardless of expertise in design, organizational research, or business innovation management.