The growing demand for wearable devices, soft robotics, and tissue engineering in recent years has led to an increased effort in the field of soft materials. With the advent of personalized devices, the one-shape-fits-all manufacturing methods may soon no longer be the standard for the rapidly increasing market of soft devices. Recent findings have pushed technology and materials in the area of additive manufacturing (AM) as an alternative fabrication method for soft functional devices, taking geometrical designs and functionality to greater heights. For this reason, this review aims to highlights recent development and advances in AM processable soft materials with self-healing, shape memory, electronic, chromic or any combination of these functional properties. Furthermore, the influence of AM on the mechanical and physical properties on the functionality of these materials is expanded upon. Additionally, advances in soft devices in the fields of soft robotics, biomaterials, sensors, energy harvesters, and optoelectronics are discussed. Lastly, current challenges in AM for soft functional materials and future trends are discussed.