Recently, there has been a growing interest in the research community about using wrist-worn devices, such as smartwatches for human activity recognition, since these devices are equipped with various sensors such as an accelerometer and a gyroscope. Similarly, smartphones are already being used for activity recognition. In this paper, we study the fusion of a wrist-worn device ( smartwatch) and a smartphone for human activity recognition. We evaluate these two devices for their strengths and weaknesses in recognizing various daily physical activities. We use three classifiers to recognize 13 different activities, such as smoking, eating, typing, writing, drinking coffee, giving a talk, walking, jogging, biking, walking upstairs, walking downstairs, sitting, and standing. Some complex activities, such as smoking, eating, drinking coffee, giving a talk, writing, and typing cannot be recognized with a smartphone in the pocket position alone. We show that the combination of a smartwatch and a smartphone recognizes such activities with a reasonable accuracy. The recognition of such complex activities can enable well-being applications for detecting bad habits, such as smoking, missing a meal, and drinking too much coffee. We also show how to fuse information from these devices in an energy-efficient way by using low sampling rates. We make our dataset publicly available in order to make our work reproducible.