For more than seven decades, the dominant ambition of computing research has been artificial intelligence (AI): machines that perform tasks which ordinarily require human intelligence. The rapid progress of deep learning, transformer-based foundation models and large-scale reinforcement learning since 2012 has moved that ambition from laboratory curiosity to everyday infrastructure. This paper argues that the next technological turn of events is not "more AI" in the incremental sense, but the possible emergence of superintelligence (ASI): systems whose cognitive performance greatly exceeds that of the best human minds across virtually all domains of interest. Using an integrative literature review of peer-reviewed scholarship, expert surveys, technical reports and policy instruments published between 1950 and 2025, the paper (i) clarifies the conceptual distinction between narrow AI, artificial general intelligence (AGI) and superintelligence; (ii) traces the intellectual history of the idea from Turing and Good to contemporary scaling research; (iii) analyses six plausible pathways to superintelligence, namely compute and data scaling, algorithmic and architectural innovation, recursive self-improvement, whole brain emulation, biological and neural-interface enhancement, and networked collective intelligence; (iv) evaluates the evidence and counter-evidence on timelines and "takeoff" speeds; (v) maps the transformative opportunities and the systemic and existential risks; and (vi) reviews emerging governance responses at global, continental and national levels, with particular attention to Africa and Nigeria. The review finds that superintelligence differs from present-day AI not merely in degree but in kind: it shifts the central problem from building capable tools to aligning and governing autonomous agents more capable than their designers. The paper proposes a Superintelligence Readiness and Governance Framework (SRGF) built on five interlocking layers: foundational capacity, technical alignment and safety, institutional governance, socio-economic transition, and international coordination. It concludes with recommendations for researchers, policymakers, industry and developing economies, and identifies priority areas for future research.