Stealing attack against controlled information, along with the increasing number of information leakage incidents, has become an emerging cyber security threat in recent years. Due to the booming development and deployment of advanced analytics solutions, novel stealing attacks utilize machine learning (ML) algorithms to achieve high success rate and cause a lot of damage. Detecting and defending against such attacks is challenging and urgent so that governments, organizations, and individuals should attach great importance to the ML-based stealing attacks. This survey presents the recent advances in this new type of attack and corresponding countermeasures. The ML-based stealing attack is reviewed in perspectives of three categories of targeted controlled information, including controlled user activities, controlled ML model-related information, and controlled authentication information. Recent publications are summarized to generalize an overarching attack methodology and to derive the limitations and future directions of ML-based stealing attacks. Furthermore, countermeasures are proposed towards developing effective protections from three aspects -- detection, disruption, and isolation.