In the rapidly evolving digital landscape, Denial of Service (DoS) and Distributed Denial of Service (DDoS) attacks continue to pose significant threats to critical infrastructure, particularly within the financial sector. This paper examines the methodologies and impacts of DoS and DDoS attacks, with a particular focus on the financial industry, highlighting vulnerabilities within critical financial operations. Various types of attacks, including volumetric, protocol, and application-layer attacks, are reviewed alongside their potential consequences on service availability and financial stability. Furthermore, the paper explores machine learning (ML) and deep learning (DL) techniques for detecting and mitigating these threats, analyzing their performance, computational efficiency, and suitability in financial contexts. The findings provide a comprehensive evaluation of these techniques and emphasize the importance of adopting a layered defense strategy to protect financial services from both high-volume and low-bandwidth attacks.