Over the last decade, metasurfaces have proven extremely useful and versatile to design a broad range of photonic systems in a very innovative way. However, most optical metasurfaces demonstrated so far rely on meta-atoms that are either in plasmonic metals (supporting predominantly electric resonances) or in high index dielectrics (supporting predominantly magnetic resonances). In this presentation, I will report on our on-going research effort to develop metasurfaces that utilize hybrid meta-atoms, combining both dielectrics and metals. This combination unleashes interesting optical effects that stem from the interaction between electric and magnetic resonances – so-called bi-anisotropy. At the same time, this poses some significant technological challenges, since both materials are difficult to combine in the same nanofabrication – especially because the resulting aspect ratio is quite high. Indeed, bi-anisotropy is magnified by thick structures. To address this technological challenge, we resort to etching the nanostructures, rather than using the more common lift-off approach, which only works well for thin, planar, geometries. Through etching, we are able to produce quite thick meta-atoms that exhibit strong bi- anisotropy, leading to significant coupling between electric and magnetic effects. Different applications are presented at optical frequencies in the linear and nonlinear regimes. In the linear regime, we consider biosensing using hybrid structures built from silicon and aluminium. In the nonlinear regime, we demonstrate a nonlinear pseudo-diode that produces a strong nonlinear response when illuminated from one side, while illumination from the other side does not produce any significant nonlinear response, similar to a diode that lets only the current pass in one direction. The presentation will emphasize the numerical challenges associated with the simulation of hybrid metasurfaces and their analysis using multipolar resonances.