Time series is one of the most commonly encountered data types, touching almost every aspect of human life, including areas such as medicine, finance, sciences, and industry. With the widespread use of sensor networks, large scale time series have become ubiquitous in both industrial processes and research applications. Finding repeated patterns, also called motifs, in those large-scale time series has become one of the most essential tasks in time series data mining. To meet the need of detecting such patterns in large-scale time series, many new efficient and robust motif discovery algorithms have been introduced in the last five years. In this tutorial, we will systematically review recent advances in the motif discovery research area and discuss the challenges faced in this research field. While the general idea of time series motifs is that they represent repeated patterns in a time series, the exact definition, objective, or metric to discover them vary. Algorithms have been proposed according to the specific motif definition or criterion. In this tutorial, we will go over different definitions and algorithms based on these definitions, as well as discussing their respective advantages and disadvantages.