The integration of 3D printed sensors into hosting structures has become a growing area of research due to simplified assembly procedures, reduced system complexity, and lower fabrication cost. Embedding 3D printed sensors into structures or bonding the sensors on surfaces are the two techniques for the integration of sensors. This review extensively discusses the fabrication of sensors through different additive manufacturing techniques. Various additive manufacturing techniques dedicated to manufacture sensors as well as their integration techniques during the manufacturing process will be discussed. This review will also discuss the basic sensing mechanisms of integrated sensors and their applications. It has been proven that integrating 3D printed sensors into infrastructures can open new possibilities for research and development in additive manufacturing and sensor materials for smart goods and the Internet of Things.