The challenge of deriving insights from the Internet of Things (IoT) has been recognized as one of the most exciting and key opportunities for both academia and industry. Advanced analysis of big data streams from sensors and devices is bound to become a key area of data mining research as the number of applications requiring such processing increases. Dealing with the evolution over time of such data streams, i.e., with concepts that drift or change completely, is one of the core issues in IoT stream mining. This tutorial is a gentle introduction to mining IoT big data streams. The first part introduces data stream learners for classification, regression, clustering, and frequent pattern mining. The second part deals with scalability issues inherent in IoT applications, and discusses how to mine data streams on distributed engines such as Spark, Flink, Storm, and Samza.