Self-Refinement refers to a model's ability to revise its own responses to produce improved outputs. This capability can also serve as a fundamental mechanism for Self-Improvement, for example, by reconstructing datasets with refined results to enhance intrinsic model performance. However, our comprehensive experiments reveal that large language models (LLMs) show no clear evidence of inherent Self-Refinement and may even experience response quality degradation after Self-Refinement. To address this issue, we propose EVOLVE, a simple and effective framework for eliciting and tracking the evolution of Self-Refinement through iterative training. We first explore optimization methods during training to activate the model's Self-Refinement capability. Then, at inference, we investigate various generation strategies to further enhance and utilize Self-Refinement while supplying the necessary data for training. Through synergistic optimization of training and inference stages, we continually evolve the model's Self-Refinement ability, enabling it to better refine its own responses. Moreover, we demonstrate the potential of leveraging Self-Refinement to achieve broader Self-Improvement of intrinsic model abilities. Experiments show that the evolved Self-Refinement ability enables the Llama-3.1-8B base model to surpass GPT-4o, achieving 62.3% length-controlled and 63.3% raw win rates on AlpacaEval 2, and 50.3% on Arena-Hard. It also generalizes effectively to out-of-domain reasoning tasks, improving performance on mathematical reasoning benchmarks such as GSM8K and MATH.