With the advent of miniaturized sensing technology, which can be body-worn, it is now possible to collect and store data on different aspects of human movement under the conditions of free living. This technology has the potential to be used in automated activity profiling systems which produce a continuous record of activity patterns over extended periods of time. Such activity profiling systems are dependent on classification algorithms which can effectively interpret body-worn sensor data and identify different activities. This article reviews the different techniques which have been used to classify normal activities and/or identify falls from body-worn sensor data. The review is structured according to the different analytical techniques and illustrates the variety of approaches which have previously been applied in this field. Although significant progress has been made in this important area, there is still significant scope for further work, particularly in the application of advanced classification techniques to problems involving many different activities.