Anomaly detection is a critical issue across several academic fields and real-world applications. Artificial neural networks have been proposed to detect anomalies from different input types, but there is no clear guide to deciding which model to use in a specific case. Therefore, this study examines the most relevant Neural Network Outlier Detection algorithms in the literature, compares their benefits and drawbacks in some application scenarios, and displays their outcomes in benchmark datasets. The initial search revealed 1422 papers on projects completed between 2017 and 2021. These papers were further narrowed based on title, abstract, quality assessment, inclusion, and exclusion criteria, remaining 76 articles. Finally, we reviewed these publications and verified that Autoencoder Neural Network, Convolutional Neural Network, Recurrent Neural Network, and Generative Adversarial Network have promisor outcomes for outlier detection, the advantages of these neural networks for outlier detection, and the significant challenges of outlier detection strategies.