Anemia is a serious public health issue affecting over 33% of the world's population. It can result in major health issues such as stunted growth in children, slowed mental and psychomotor development, worse work performance, and increased susceptibility to parasite infections. It is caused by various reasons, including dietary problems, blood disorders, infections and some genetic diseases. Traditional invasive detection methods are expensive, and the results although dependable and accurate but it takes a lot of time, therefore novel, non-invasive methods of detecting and diagnosing anemia are needed. This paper presents a narrative review of research studies interested in the non-invasive detection and diagnosing of anemia and introduces a comparative analysis of how accurate the diagnosing results are. Moreover, it reveals a trend in research towards an increasing interest in detecting and diagnosing anemia non-invasively by applying different artificial intelligence algorithms on eye conjunctiva, fingernails and hand palm images. Researchers utilized different AI algorithms such as Convolutional Neural Networks, Support Vector Machines, Decision Trees, k-Nearest Neighbor, Naïve Bayes, Logistic regression, random forest, AlexNet, ELM, XGBOOST, LGMBoost, RESNet-50, MobileNet20, EfficientNet-B3, Dense Net 121, CNN Allnet, and ANN. Results of the comparative analysis indicate that the hand palm is the most reliable body region for anemia detection, and the Naïve Bayes is the best algorithm with diagnosing accuracy of 99.96%. This narrative review shows that using non-invasive approach for detecting and diagnosing anemia could provide a possible reliable alternative for quick, affordable anemia screening, especially in non-clinical and low-resource countries.