Radar technology has seen substantial progression over the past decades, growing into a vital component supporting important applications across diverse industries including aviation, meteorology, defense, and autonomous systems. This holistic evaluation aims to provide an in-depth exploration of recent progress and persisting barriers related to radar signal processing. Key topics analyzed in detail include advanced signal processing methodologies, target detection and multitarget tracking algorithms, high-resolution radar imaging techniques, and synergistic integration of radar with modern technologies. By surveying state-of-the-art developments and identifying existing challenges, this review intends to underline the critical function of radar information processing in transforming sensing and perception capabilities across multiple sectors. Through examining cutting-edge research and emerging trends, insights are gleaned around how resilient and optimized radar systems can be designed to overcome longstanding limitations. This evaluation also highlights how the seamless integration of radar with complementary sensors and computational advancements will advance situational awareness to unprecedented levels. It is hoped that the holistic treatment of progress and deficiencies presented herein will help stimulate further discovery toward realizing the full promise of radar to beneficially impact diverse applications relying on accurate environmental awareness and perception.