Alzheimer's disease (AD) is the most common form of dementia and is characterized by progressive memory loss, impairment of other cognitive functions, and inability to perform activities of daily life. The key to understanding AD aetiology lies in the development of effective disease models, which should ideally recapitulate all aspects pertaining to the disease. A plethora of techniques including in vivo, in vitro, and in silico platforms have been utilized in developing disease models of AD over the years. Each of these approaches has revealed certain essential characteristics of AD; however, none have managed to fully mimic the pathological hallmarks observed in the AD human brain. In this review, we will provide details into the genesis, evolution, and significance of the principal methods currently employed in modelling AD, the advantages and limitations faced in their application, including the headways made by each approach. This review will focus primarily on two-dimensional and three-dimensional in vitro modelling of AD, which during the last few years has made significant breakthroughs in the areas of AD pathology and therapeutic screening. In addition, a glimpse into state-of-the-art neural tissue engineering techniques incorporating biomaterials and microfluidics technologies is provided, which could pave the way for the development of more accurate and comprehensive AD models in the future.