Automatic modulation classification (AMC) is a key component of spectrum awareness, cognitive radio, and signal intelligence, enabling receivers to identify modulation schemes from noisy in-phase and quadrature (IQ) observations. Traditional approaches rely on likelihood-based methods or handcrafted feature extraction, which often struggle under channel impairments and real-world variability. Recent advances in deep learning enable models to learn directly from multiple signal representations, including raw IQ samples, engineered features, and time–frequency or constellation-based encodings, improving adaptability across diverse signal conditions. This paper presents a structured review of deep learning approaches for AMC, including CNNs, RNN/LSTM models, and transformer-based architectures, with a focus on performance, robustness, and system-level trade-offs. We analyze how representation choices, dataset design, and evaluation protocols influence reported results, and highlight key challenges such as domain shift, low-SNR environments, and multi-signal interference. Finally, we outline future directions focused on improving generalization, integrating classical signal processing with learning-based methods, and enabling efficient deployment in real-world and resource-constrained systems.