Discoveries in the field of medical sciences are blooming rapidly at the cost of voluminous efforts. Presently, multidisciplinary research activities have been especially contributing to catering cutting-edge solutions to critical problems in the domain of medical sciences. The modern age computing resources have proved to be a boon in this context. Effortless solutions have become a reality, and thus, the real beneficiary patients are able to enjoy improved lives. One of the most emerging problems in this context is Alzheimer's disease, an incurable neurological disorder. For this, early diagnosis is made possible with benchmark computing tools and schemes. These benchmark schemes are the results of novel research contributions being made intermittently in the timeline. In this review, an attempt is made to explore all such contributions in the past few decades. A systematic review is made by categorizing these contributions into three folds, namely, First, Second, and Third Generations. However, priority is given to the latest ones as a handful of literature reviews are already available for the classical ones. Key contributions are discussed vividly. The objectives set for this review are to bring forth the latest discoveries in computing methodologies, especially those dedicated to the diagnosis of Alzheimer's disease. A detailed timeline of the contributions is also made available. Performance plots for certain key contributions are also presented for better graphical understanding.