Machine learning and statistical algorithms are receiving considerable attention during the past decade in prognostics and health management (PHM). However, there is a lack of consensus and methodology on algorithm selection in different scenarios, which renders the random implementation of machine learning algorithms and inefficient development processes. PHM Data Challenge, an open data competition specialized in PHM, includes diverse issues in industrial data analytics and thus provides abundant resources for study and appropriate approach development. In this work, we first summarize the problems and datasets of PHM Data Challenge competitions. According to their objectives, the 9 problems can be classified into 3 categories, health assessment, fault classification, and remaining useful life prediction. Second, common issues and unique challenges have been clearly pointed out for each problem and each category. Then, we analyze all solutions regarding what type of strategy a particular solution took, what algorithms it used and how it overcame the challenges. At last, insights in PHM solution strategies have been summarized to conclude the paper.