Log anomaly detection is a typical core application scenario of artificial intelligence for IT operations (AIOPS) in the current data center. With the rapid development and gradual maturity of machine learning technology, the application of machine learning to log anomaly detection has become a hot spot. Firstly, this study introduces the general procedure of log anomaly detection and points out the technical classifications and typical methods in the related process. Secondly, the classifications and characteristics of the application of machine learning technology in log analysis tasks are discussed, and we probe into the technical difficulties of log analysis tasks in terms of log instability, noise interference, computation & storage requirements, and algorithm portability. Thirdly, the related research productions in the field are summarized and their technical characteristics are compared and analyzed. Finally, the study discusses the future research focus and thinking of log anomaly detection from three aspects: log semantic representation, online model update, algorithm parallelism and versatility.