Phishing detection with high-performance accuracy and low computational complexity has always been a topic of great interest. New technologies have been developed to improve the phishing detection rate and reduce computational constraints in recent years. However, one solution is insufficient to address all problems caused by attackers in cyberspace. Therefore, the primary objective of this paper is to analyze the performance of various deep learning algorithms in detecting phishing activities. This analysis will help organizations or individuals select and adopt the proper solution according to their technological needs and specific applications’ requirements to fight against phishing attacks. In this regard, an empirical study was conducted using four different deep learning algorithms, including deep neural network (DNN), convolutional neural network (CNN), Long Short-Term Memory (LSTM), and gated recurrent unit (GRU). To analyze the behaviors of these deep learning architectures, extensive experiments were carried out to examine the impact of parameter tuning on the performance accuracy of the deep learning models. In addition, various performance metrics were measured to evaluate the effectiveness and feasibility of DL models in detecting phishing activities. The results obtained from the experiments showed that no single DL algorithm achieved the best measures across all performance metrics. The empirical findings from this paper also manifest several issues and suggest future research directions related to deep learning in the phishing detection domain.