Material efficiency (ME) strategies are pursued by governments and companies to reduce environmental emissions, improve supply chain resilience, and enhance cost competitiveness. Material flow analysis (MFA) methods are useful to quantify raw material stocks and flows and assess the potential impacts of ME strategies. Although the popularity of MFA methods is increasing, there are methodological limitations that hinder its use as a decision support tool for prospective assessments. To overcome some of these, MFA is increasingly integrated with other methods from different research fields. This paper categorizes integrated MFA methods by identifying and explaining the methods and their applications. A semi-structured literature review screened a wide range of methods integrated with MFA prospective analysis and evaluated their applications from 158 studies. This showed that integrated MFA can be used to: (1) include economic, social, and environmental layers; (2) improve the technical foundation of MFA by including entropy and exergy analyses and process engineering methods; (3) include economic mechanisms and link the economic system to the material system; and (4) improve the representation of materials in existing methods and models. Our research demonstrates that integrated MFA should be a central method in planning and designing ME strategies for companies and governments. This paper provides an important knowledge base of integrated MFA methods and creates a discussion point on MFA, where the research field is currently at or indeed where it could be heading in the future, that is, "Quo Vadis" MFA.