The purpose of this article is to gather recent findings about the non-linear dynamics of distributed feedback quantum cascade lasers, with a view on practical applications in a near future. As opposed to other semiconductor lasers, usually emitting in the visible or the near-infrared region, quantum cascade laser technology takes advantage of intersubband transitions and quantum engineering to emit in the mid-infrared and far-infrared domain. This peculiarity and its physical consequences were long considered as a detrimental characteristic to generate non-linear dynamics under external optical control. However, we show that a wide diversity of phenomena, from high-dimensional chaos to giant pulses can be observed when the quantum cascade laser is under external optical feedback or under optical injection and with a continuous current bias. Most of these phenomena have already been observed in other semiconductor lasers under optical feedback or under optical injection, which allows us comparing quantum cascade lasers with their interband counterparts.