Given the large size and volumes of contracts and their underlying inherent complexity, manual reviews become inefficient and prone to errors, creating a clear need for automation. Automatic Legal Contract Classification (LCC) revolutionizes the way legal contracts are analyzed, offering substantial improvements in speed, accuracy, and accessibility. This survey delves into the challenges of automatic LCC and a detailed examination of key tasks, datasets, and methodologies. We identify seven classification tasks within LCC, and review fourteen datasets related to English-language contracts, including public, proprietary, and non-public sources. We also introduce a methodology taxonomy for LCC, categorized into Traditional Machine Learning, Deep Learning, and Transformer-based approaches. Additionally, the survey discusses evaluation techniques and highlights the best-performing results from the reviewed studies. By providing a thorough overview of current methods and their limitations, this survey suggests future research directions to improve the efficiency, accuracy, and scalability of LCC. As the first comprehensive survey on LCC, it aims to support legal NLP researchers and practitioners in improving legal processes, making legal information more accessible, and promoting a more informed and equitable society.