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Physical activity recognition using embedded sensors has enabled many context-aware applications in different areas, such as healthcare. Initially, one or more dedicated wearable sensors were used for such applications. However, recently, many researchers started using mobile phones for this purpose, since these ubiquitous devices are equipped with various sensors, ranging from accelerometers to magnetic field sensors. In most of the current studies, sensor data collected for activity recognition are analyzed offline using machine learning tools. However, there is now a trend towards implementing activity recognition systems on these devices in an online manner, since modern mobile phones have become more powerful in terms of available resources, such as CPU, memory and battery. The research on offline activity recognition has been reviewed in several earlier studies in detail. However, work done on online activity recognition is still in its infancy and is yet to be reviewed. In this paper, we review the studies done so far that implement activity recognition systems on mobile phones and use only their on-board sensors. We discuss various aspects of these studies. Moreover, we discuss their limitations and present various recommendations for future research.