We have investigated the emission properties of InAs/GaAs self-assembled quantum dots in the mid-infrared. The emission relies on the intraband transitions in the valence band of the quantum dots. We first show that third-harmonic generation can be observed. The frequency tripling efficiency is enhanced by the resonances between the pump excitation and the quantum dot intraband transitions. A giant third-order nonlinear susceptibility is measured for one dot plane. The narrow spectral dependence of the nonlinear susceptibility is well explained by simulations which account for the three-dimensional confinement potential. We secondly show that the mid-infrared spontaneous emission between hole confined states can be observed under an interband optical pumping. The spontaneous emission involves transitions between either the ground and excited states or between excited states. These measurements demonstrate the potentiality of self-assembled quantum dots for mid-infrared emission.