Precision livestock farming (PLF) research is rapidly increasing and has improved farmers’ quality of life, animal welfare, and production efficiency. PLF research in dairy calves is still relatively recent but has grown in the last few years. Automatic milk feeding systems (AMFS) and 3D accelerometers have been the most extensively used technologies in dairy calves. However, other technologies have been emerging in dairy calves’ research, such as infrared thermography (IRT), 3D cameras, ruminal bolus, and sound analysis systems, which have not been properly validated and reviewed in the scientific literature. Thus, with this review, we aimed to analyse the state-of-the-art of technological applications in calves, focusing on dairy calves. Most of the research is focused on technology to detect and predict calves’ health problems and monitor pain indicators. Feeding and lying behaviours have sometimes been associated with health and welfare levels. However, a consensus opinion is still unclear since other factors, such as milk allowance, can affect these behaviours differently. Research that employed a multi-technology approach showed better results than research focusing on only a single technique. Integrating and automating different technologies with machine learning algorithms can offer more scientific knowledge and potentially help the farmers improve calves’ health, performance, and welfare, if commercial applications are available, which, from the authors’ knowledge, are not at the moment.