Recent advancements in Large Language Models (LLMs) have highlighted significant developments in self-evolution capabilities and integration with advanced algorithms. A comprehensive survey on self-evolution in LLMs suggests that this area is an emerging paradigm with much to solve. AlphaLLM, a notable development, integrates Monte Carlo Tree Search (MCTS) with LLMs to enable autonomous self-improvement. This approach allows LLMs to autonomously acquire, refine, and learn from their own generated experiences, mimicking human experiential learning without intensive human supervision. Additionally, the integration of LLMs with software engineering is poised to transform access to computer programming, making it accessible to anyone who can write structured English. Moreover, DeepMind researchers have discovered impressive learning capabilities in long-context LLMs, further enhanced by self-playing adversarial language games.