Nonlinear control methods are essential for effective control of complicated dynamic systems, particularly when conventional linear techniques are ineffective. The paper presents an extensive review of contemporary nonlinear control techniques, paying particular attention to their categorization, theoretical backgrounds, and real-world applications. The study starts with the introduction of nonlinear system properties and mathematical modeling, followed by a bibliometric analysis that illustrates the increasing popularity of the research topic. The article classifies nonlinear control methodologies into two broad categories: system linearization-based and nonlinear control law-based direct approaches. Adaptive control, Nonlinear Model Predictive Control, and Artificial Intelligence-based control methodologies are investigated in detail and systematically compared based on recent experimental findings. Particular emphasis is placed on novel developments, e.g., data-driven control methods and optimization-based techniques, which have shown encouraging results in practical applications. The results emphasize the growing role of machine learning and model-free methods in nonlinear control. The review is a valuable resource for researchers and practitioners interested in getting acquainted with state-of-the-art nonlinear control techniques and their changing background.