Phishing attacks pose a significant cybersecurity threat, with malicious actors continually evolving their tactics to deceive users and steal sensitive information. This research conducted a comparative analysis of machine learning (ML) algorithms, specifically Support Vector Machines (SVM) and Decision Trees, alongside deep learning Long Short-Term Memory Networks (LSTMs) for detecting phishing website URLs. Utilizing a dataset containing features extracted from URLs, we trained and evaluated the performance of these algorithms based on accuracy, precision, recall, and F1 score. The study also investigated the interpretability, computational complexity, and generalization capabilities of the models. Our findings indicated that LSTMs outperformed SVMs and Decision Trees, offering a balanced approach with low false positive and false negative rates. This balance was crucial in phishing detection, where the cost of missing a phishing attempt could be as severe as wrongly blocking legitimate access. The results underscored the importance of selecting a machine learning model based on the specific requirements and constraints of the phishing detection system, providing valuable guidance for cybersecurity practitioners and researchers in developing effective defense mechanisms against phishing attacks.