Recent years have seen a dramatic rise in the use of passive acoustic monitoring (PAM) for biological and ecological applications, and a corresponding increase in the volume of data generated. However, data sets are often becoming so sizable that analysing them manually is increasingly burdensome and unrealistic. Fortunately, we have also seen a corresponding rise in computing power and the capability of machine learning algorithms, which offer the possibility of performing some of the analysis required for PAM automatically. Nonetheless, the field of automatic detection of acoustic events is still in its infancy in biology and ecology. In this review, we examine the trends in bioacoustic PAM applications, and their implications for the burgeoning amount of data that needs to be analysed. We explore the different methods of machine learning and other tools for scanning, analysing, and extracting acoustic events automatically from large volumes of recordings. We then provide a step-by-step practical guide for using automatic detection in bioacoustics. One of the biggest challenges for the greater use of automatic detection in bioacoustics is that there is often a gulf in expertise between the biological sciences and the field of machine learning and computer science. Therefore, this review first presents an overview of the requirements for automatic detection in bioacoustics, intended to familiarise those from a computer science background with the needs of the bioacoustics community, followed by an introduction to the key elements of machine learning and artificial intelligence that a biologist needs to understand to incorporate automatic detection into their research. We then provide a practical guide to building an automatic detection pipeline for bioacoustic data, and conclude with a discussion of possible future directions in this field.