To unlock the potential for corporations to play a more proactive role in sustainable development, it is critical to have a fundamental understanding of the pathways leading to a responsible and sustainable business. This study explores contributions of theories of the firm in explicating why and how integrating corporate social responsibility (CSR) and corporate sustainability (CS) into business strategic decisions and operation processes helps to improve the viability of corporations. The research objective is addressed through a narrative review of relevant literature by following the developmental and evolutionary sequences in business responsibility and sustainability while contemplating the connections between CSR and CS through the lens of the dominant theoretical perspectives underpinning the concepts. The study posits an integrative theoretical framework that offers supports for embedding CSR and CS into a corporate business strategy. It discusses that corporate choice of CSR and CS actions and policies is supported by dual internal and external mechanisms based on resource-based theory and institutional theory. This is to meet the interests and expectations of internal and external stakeholders, the basis upon which stakeholder theory is constructed. Findings from this review corroborate the proposition that the three theories of resource-based, institutional, and stakeholder could be used as the primary approach to explain corporate recognition of the need for CSR and CS, and further build a coherent platform to support corporate choice and adoption of CSR and CS in business strategy.