Legal prediction presents one of the most significant challenges when applying artificial intelligence (AI) to the legal field. The legal system is a complex adaptive system characterized by the ambiguity of legal language and the diversity of value functions. The imprecision and procedural knowledge inherent in law makes judicial issues difficult to be expressed in a computer symbol system. Current semantic processing and machine learning technologies cannot fully capture the complex nature of legal relations, thereby raising doubts about the accuracy of legal predictions and reliability of judicial models. Cognitive computing, designed to emulate human brain functions and aid in enhancing decision-making processes, offers a better understanding of legal data and the processes of legal reasoning. This paper discusses the advancements made in cognitive methods applied to legal concept learning, semantic extraction, judicial data processing, legal reasoning, understanding of judicial bias, and the interpretability of judicial models. The integration of cognitive neuroscience with law has facilitated several constructive attempts, indicating that the evolution of cognitive law could be the next frontier in the intersection of AI and legal practice.