In recent years, recommendation systems have gained significant importance due to the vast amount of digital content available on various online platforms. Collaborative filtering is a widely adopted approach in recommendation systems, leveraging user-item interactions to make personalized predictions. However, traditional collaborative filtering methods face challenges such as the cold-start problem and data sparsity. To address these issues, researchers have proposed advanced techniques, including Adaptive KNN-Based and SVD-Based Extended Collaborative Filtering. This paper provides a comprehensive review of these two recommendation systems, discussing their underlying principles, advantages, and limitations. Furthermore, we explore recent research advancements and real-world applications, providing insights into the potential future developments in this field.