Silicon-organic hybrid (SOH) devices combine silicon waveguides with a number of specialized materials, ranging from third-order optically-nonlinear molecules to second-order nonlinear polymers and liquid-crystals. Second-order nonlinear materials allow building high-speed and low-voltage electro-optic modulators, which are key components for future silicon-based photonics transceivers. We report on a 90 GHz bandwidth phase modulator, and on a 56 Gbit/s QPSK experiment using an IQ Pockels effect modulator. By using liquid-crystal claddings instead, we show experimentally that phase shifters with record-low power consumption and ultra-low voltage-length product of V π L = 0.06 Vmm. Secondorder nonlinear materials, moreover, allow creating nonlinear waveguides for sum-or difference-frequency generation, and for lowest-noise optical parametric amplification. These processes are exploited for a large variety of applications, like in the emerging field of on-chip generation of mid-IR wavelengths, where pump powers are significantly smaller compared to equivalent devices using third-order nonlinear materials. In this work, we present the first SOH waveguide design suited for second-order nonlinear processes. We predict for our device an amplification of 14 dB/cm assuming a conservative χ (2) -nonlinearity of 230 pm/V and a CW pump power as low as 20 dBm.