We develop a generalized Gross-Pitaevskii approach to the driven-dissipative dynamics of intersubband polaritons in patterned planar microcavities where the cavity mode is strongly coupled to an intersubband transition in doped quantum wells. Substantial differences with respect to the case of interband excitonic polaritons are highlighted, in particular the non-Markovian features of the radiative decay. The accuracy of the method is validated on the linear reflection properties of the cavity, that quantitatively reproduce experimental observations. The theoretical framework is then applied in the nonlinear regime to study optical parametric oscillation processes for intersubband polaritons. Our findings open interesting perspectives in view of novel coherent laser sources operating in the mid and far infrared.Planar semiconductor microcavities have emerged as a versatile tool to address fundamental questions in the physics of light-matter interaction, and realize a new generation of optoelectronic devices, with applications that are still largely unexplored [1]. In particular, a rich variety of optical phenomena are observed when a quantum well element is embedded in the cavity layer and an electronic transition is resonantly coupled to the cavity mode. Depending on the structure and the doping level of the quantum well, the transition can be of either inter-band [2] or inter-subband nature [3]: in the former case, it involves some electrons being promoted from the valence to the conduction band and is typically located in the near-infrared or visible domain. In the latter case, electrons (or holes) are promoted from a filled subband of the conduction (or valence) band to another, initially empty subband. For a strong enough light-matter coupling, photons can undergo several absorption-emission cycles before being lost. In this so-called strong lightmatter coupling regime, the eigenmodes are superpositions of photonic and matter excitations: depending on the nature of the electronic transition involved, we usually speak of interband polaritons or intersubband polaritons.As a few decades of intense theoretical and experimental research have shown, interband (IB) polaritons combine the extremely low mass of cavity photons (orders of magnitude lower than the excitonic one) with sizable interactions stemming from their excitonic component. These remarkable properties have been at the heart of the celebrated observations of Bose-Einstein condensation [4] and superfluidity effects [5,6] in a polariton gas and are still being widely exploited in a number of exciting directions, as reviewed in [1,7,8].Since with the early observations [9, 10], the research on intersubband (ISB) polaritons has also made impressive steps. In addition to their operation at much longer wavelengths in the mid or far infrared spectively), ISB polaritons display a few other remarkable differences compared to IB ones. Since a large number of electrons are involved in the optical transition, the Rabi splitting can be pushed to extremely high val...