Ontologies are widely used to formally represent abstract domain knowledge. Logic reasoning ensures the logical consistency of ontologies, and infers knowledge implicitly encoded in ontologies. It has been shown both theoretically and empirically that for large and complex ontologies, reasoning is still time-consuming and resource-intensive. Meta-reasoning exploits machine learning techniques to tackle the important problems of understanding the source of reasoning hardness and to predict reasoning efficiency, with the overall goal of improving reasoning efficiency. In this paper, we highlight recent advances in meta-reasoning for Semantic Web ontologies, briefly present technical innovations and results, and discuss important problems for future research.