Recurrent Neural Networks are powerful machine learning frameworks that allow for data to be saved and referenced in a temporal sequence. This opens many new possibilities in fields such as handwriting analysis and speech recognition. This paper seeks to explore current research being conducted on RNNs in four very important areas, being biometric authentication, expression recognition, anomaly detection, and applications to aircraft. This paper reviews the methodologies, purpose, results, and the benefits and drawbacks of each proposed method below. These various methodologies all focus on how they can leverage distinct RNN architectures such as the popular Long Short-Term Memory (LSTM) RNN or a Deep-Residual RNN. This paper also examines which frameworks work best in certain situations, and the advantages and disadvantages of each proposed model.