Time series classification is a subfield of machine learning with numerous real-life applications. Due to the temporal structure of the input data, standard machine learning algorithms are usually not well suited to work on raw time series. Over the last decades, many algorithms have been proposed to improve the predictive performance and the scalability of state-of-the-art models. Many approaches have been investigated, ranging from deriving new metrics to developing bag-of-words models to imaging time series to artificial neural networks. In this review, we present in detail the major contributions made to this field and mention their most prominent extensions. We dedicate a section to each category of algorithms, with an intuitive introduction on the general approach, detailed theoretical descriptions and explicit illustrations of the major contributions, and mentions of their most prominent extensions. At last, we dedicate a section to publicly available resources, namely data sets and open-source software, for time series classification. A particular emphasis is made on enumerating the availability of the mentioned algorithms in the most popular libraries. The combination of theoretical and practical contents provided in this review will help the readers to easily get started on their own work on time series classification, whether it be theoretical or practical.