A key strategy in machine learning is to break down a problem into smaller and more manageable parts, then process data or unknown variables recursively. Sequential Monte Carlo (SMC) is a technique for solving statistical inference problems recursively. Over the last 20 years, SMC has been developed to enabled inference in increasingly complex and challenging models in Signal Processing and Statistics. This monograph shows how the powerful technique can be applied to machine learning problems such as probabilistic programming, variational inference and inference evaluation to name a few. Written in a tutorial style, Elements of Sequential Monte Carlo introduces the basics of SMC, discusses practical issues, and reviews theoretical results before guiding the reader through a series of advanced topics to give a complete overview of the topic and its application to machine learning problems. This monograph provides an accessible treatment for researchers of a topic that has recently gained significant interest in the machine learning community.