Global demographics trend toward an aging population. Hence, there will be an increased social demand for elderly care. Recently, assistive technologies such as service robots have emerged and can help older adults to live independently. This paper reports a review starting from 1999 of the existing mobile service robots used for older adults to grow old at home. We describe each robot from the viewpoint of applications, platforms, and empirical studies. Studies reported that mobile social robots could assist older adults throughout their daily activities such as reminding, household tasks, safety, or health monitoring. Moreover, some of the reported studies indicate that mobile service robots can enhance the well-being of older adults and decrease the workload for their caregivers.