This paper presents a comprehensive survey of sentiment analysis methods for movie reviews, a benchmark task that has played a central role in advancing natural language processing. We review the evolution of techniques from early lexicon-based and classical machine learning approaches to modern deep learning architectures and large language models, covering widely used datasets such as IMDb, Rotten Tomatoes, and SST-2, and models ranging from Naive Bayes and support vector machines to LSTM networks, BERT, and attention-based transformers. Beyond summarizing prior work, this survey differentiates itself by offering a comparative, challenge-driven analysis of how these modeling paradigms address domain-specific issues such as sarcasm, negation, contextual ambiguity, and domain shift, which remain open problems in existing literature. Unlike earlier reviews that focus primarily on text-only pipelines, we also synthesize recent advances in multimodal sentiment analysis that integrate textual, audio, and visual cues from movie trailers and clips. In addition, we examine emerging concerns related to interpretability, fairness, and robustness that are often underexplored in prior surveys, and we outline future research directions including zero-shot and few-shot learning, hybrid symbolic--neural models, and real-time deployment considerations. Overall, this abstract provides a domain-focused roadmap that highlights both established solutions and unresolved challenges toward building more accurate, generalizable, and explainable sentiment analysis systems for movie review data.