Dynamic fuzzy characteristics are ubiquitous in a lot of scientific and engineering problems. Specifically, the physical systems and learning processes in machine learning are dynamic and fuzzy in general. This fact has driven researchers to integrate dynamic elements into fuzzy theory and proposed dynamic fuzzy sets and dynamic fuzzy logic. Based on these pioneering theoretical works and various theories for uncertain datasets, an innovative machine learning paradigm that is referred to as dynamic fuzzy machine learning (DFML) was proposed in the early 2000s. DFML extends existing fuzzy machine learning paradigms to deal with dynamic fuzzy problems in machine learning activities. This article provides an insightful overview of DFML by surveying the field from basics to advances in five aspects: (1) the theoretical basics; (2) the system and the learning model; (3) typical DFML methods and categorization of the methods; (4) the open challenges; and (5) the research frontiers. As the first survey addressing the topic, this article intends to help more researchers better understand the basics and state-of-the-art in this field, find the most appropriate tools for a particular application, and identify possible directions for future research.