This chapter reviews empirical studies on weak form of efficiency with the aim of establishing whether the African market is inefficient or adaptive. The reviewed studies are categorised based on their methodological approaches to compare the power of linear and non-linear models in testing for weak-form efficiency. The studies on calendar anomalies, an indication of weak-form inefficiency, are reviewed to assess whether these anomalies are adaptive as portrayed by the relatively recent theory of adaptive market hypothesis (AMH). The scope of reviewed studies is also extended to developed and emerging markets to gain a broad comparison of the findings. This review revealed that non-linear dependence has been revealed in stock returns suggesting that non-linear models are best fit to test for the stock market efficiency. Reviewed studies produced contradictory findings with some supporting and others rejecting weak-form efficiency. Thus, most studies support the AMH, which suggests that market efficiencies and anomalies are time changing. This chapter concludes that most of the existing studies on AMH have been carried out in markets other than Africa, and hence, further empirical studies on the evolving and changing nature of efficiency in African stock markets are recommended.