To ensure secure and reliable communication in wireless systems, authenticating the identities of numerous nodes is imperative. Traditional cryptography-based authentication methods suffer from issues such as low compatibility, reliability, and high complexity. Physical-Layer Authentication (PLA) is emerging as a promising complement due to its exploitation of unique properties in wireless environments. Recently, Machine Learning (ML)-based PLA has gained attention for its intelligence, adaptability, universality, and scalability compared to non-ML approaches. However, a comprehensive overview of state-of-the-art ML-based PLA and its foundational aspects is lacking. This paper presents a comprehensive survey of characteristics and technologies that can be used in the ML-based PLA. We categorize existing ML-based PLA schemes into two main types: multi-device identification and attack detection schemes. In deep learning-based multi-device identification schemes, Deep Neural Networks are employed to train models, avoiding complex processing and expert feature transformation. Deep learning-based multi-device identification schemes are further subdivided, with schemes based on Convolutional Neural Networks being extensively researched. In ML-based attack detection schemes, receivers utilize intelligent ML techniques to set detection thresholds automatically, eliminating the need for manual calculation or knowledge of channel models. ML-based attack detection schemes are categorized into three sub-types: Supervised Learning, Unsupervised Learning, and Reinforcement Learning. Additionally, we summarize open-source datasets used for PLA, encompassing Radio Frequency fingerprints and channel fingerprints. Finally, this paper outlines future research directions to guide researchers in related fields.