Proteins function as integral actors in essential life processes, rendering the realm of protein research a fundamental domain that possesses the potential to propel advancements in pharmaceuticals and disease investigation. Within the context of protein research, an imperious demand arises to uncover protein functionalities and untangle intricate mechanistic underpinnings. Due to the exorbitant costs and limited throughput inherent in experimental investigations, computational models offer a promising alternative to accelerate protein function annotation. In recent years, protein pre-training models have exhibited noteworthy advancement across multiple prediction tasks. This advancement highlights a notable prospect for effectively tackling the intricate downstream task associated with protein function prediction. In this review, we elucidate the historical evolution and research paradigms of computational methods for predicting protein function. Subsequently, we summarize the progress in protein and molecule representation as well as feature extraction techniques. Furthermore, we assess the performance of machine learning-based algorithms across various objectives in protein function prediction, thereby offering a comprehensive perspective on the progress within this field.