Since the discovery that tightly focused femtosecond laser pulses can induce a highly localised and permanent refractive index modification in a large number of transparent dielectrics, the technique of ultrafast laser inscription has received great attention from a wide range of applications. In particular, the capability to create three-dimensional optical waveguide circuits has opened up new opportunities for integrated photonics that would not have been possible with traditional planar fabrication techniques because it enables full access to the many degrees of freedom in a photon. This paper reviews the basic techniques and technological challenges of 3D integrated photonics fabricated using ultrafast laser inscription as well as reviews the most recent progress in the fields of astrophotonics, optical communication, quantum photonics, emulation of quantum systems, optofluidics and sensing.