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This paper surveys the current research directions of activity recognition using inertial sensors, with potential application in healthcare, wellbeing and sports. The analysis of related work is organized according to the five main steps involved in the activity recognition process: preprocessing, segmentation, feature extraction, dimensionality reduction and classification. For each step, we present the main techniques utilized, their advantages and drawbacks, performance metrics and usage examples. We also discuss the research challenges, such as user behavior and technical limitations, as well as the remaining open research questions.