Human activity detection within smart homes is one of the basis of unobtrusive wellness monitoring of a rapidly aging population in developed countries. Most works in this area use the concept of “activity” as the building block with which to construct applications such as healthcare monitoring or ambient assisted living. The process of identifying a specific activity encompasses the selection of the appropriate set of sensors, the correct preprocessing of their provided raw data and the learning/reasoning using this information. If the selection of the sensors and the data processing methods are wrongly performed, the whole activity detection process may fail, leading to the consequent failure of the whole application. Related to this, the main contributions of this review are the following: first, we propose a classification of the main activities considered in smart home scenarios which are targeted to older people’s independent living, as well as their characterization and formalized context representation; second, we perform a classification of sensors and data processing methods that are suitable for the detection of the aforementioned activities. Our aim is to help researchers and developers in these lower-level technical aspects that are nevertheless fundamental for the success of the complete application.