Activity recognition systems utilise data from sensors in mobile, environmental and wearable devices, ubiquitously available to individuals. It is a growing research area within intelligent systems that aims to model and identify human physical, cognitive and social actions, patterns and skills. They typically rely on supervised machine-learning approaches, in which the cost of gathering and labelling data is high due to the diverse, interleaved and dynamic nature of human behaviour. Transfer learning is an approach in which previously learned knowledge is utilised to model a new but related setting. For instance, it can reuse existing knowledge to recognise activities performed by different types of users, using different sensor technologies and in different environmental conditions. As the adoption of Internet of Thing devices increases, mobile and wearable sensing is becoming pervasive, and more challenging behaviour recognition activities are being tackled. Yet, the availability of more data does not necessarily translate to better recognition models, if these data are not properly labelled. Thus, the importance of taking advantage of transfer learning to advance the field of activity recognition. This literature review summarises the transfer learning techniques and explores the benefits of combining mobile and wearable devices with environmental sensors in support of transfer learning. We also discuss the maturity of transfer learning by analysing the validation method used in the papers reviewed. Overall, 170 selected articles published between 2014 and 2019 were reviewed following the Okali and Schabram methodology. Findings show an increase of 41% of publications when comparing the output of 2019 against the average number of papers published in the previous 5 years (2014-2018). Inertial sensors such as accelerometers and gyroscopes, are the most frequently used. Feature and instance representation are mature techniques for transfer knowledge. Unsupervised learning across users is a typical application, and shallow techniques and active learning are areas of opportunity in transfer learning methodologies.