The faithful bidirectional quantum coherent conversion of microwave (5 GHz) and optical (193.5 THz) quantum states will become essential for future quantum networks. Due to their low transition frequency, qubit states are quickly destroyed at room temperature, because of the strong microwave component of the room temperature black-body radiation. Thus, for future long-distance communication, they must be converted to the optical domain, where black-body radiation is negligible. In fact, optical photons are already largely used as information carriers in the well-established classical telecommunication industry. This type of transmission in optical fibers largely overcomes the performance of formerly used coaxial cables in terms of bandwidth, speed and propagation loss. To bridge the considerable energy gap between the optical and the microwave domain, quantum coherent microwave-optical transducers are developed in order to reliably convert microwave and optical photons at the single photon level while preserving the phase of these quantum states. The quantum transducer is in fact the quantum counterpart of the classical electro-optic modulator already used in data centers. Consequently, such a transducer can then also be used for a variety of other classical and quantum applications, such as for optical control and readout of superconducting qubits or classical microwave signals, optically heralded qubit-qubit entanglement, secure quantum communications, or for the measurement of very low microwave signals in astronomy. Several approaches to quantum transduction do exist. However, all of them show different performances in terms of conversion efficiency, bandwidth and added noise, and none of them clearly outperforms the others for all the relevant figures of merit. In this work, we focus on direct electro-optic transduction, which makes use of a material with a large chi2 nonlinearity (also known as Pockels effect) to convert the signals. The electro-optic material is chosen to be barium titanate (BaTiO3), as its Pockels effect is over 10 times stronger than the commonly used lithium niobate (LiNbO3) material in the field. We demonstrate electro-optic transduction on an integrated device made of a system of coupled BaTiO3 ring resonators, themselves capacitively coupled to an inductance-capacitance (LC) niobium resonator. In the pursuit of larger conversion efficiency and determining its material limitations, we make a detailed characterization of the electro-optic properties of BaTiO3 ridge waveguides and determine their optical absorption loss. While determining the absorption, we also simultaneously measure the Kerr nonlinearity of BaTiO3. We also develop and study the electro-optic properties of a heterogeneously integrated BaTiO3 photonic platform based on wafer-bonding of BaTiO3-on-silicon wafers to low-loss silicon nitride optical waveguides. Finally, motivated by very promising findings in bulk strontium titanate (SrTiO3), we carry out the first measurements of the electro-optic properties of integrated SrTiO3 waveguides at cryogenic temperatures (150 mK). Unlike bulk SrTiO3, which remains in a quantum paraelectric state at cryogenic temperatures, our SrTiO3 waveguides exhibit a ferroelectric phase with a remarkably large, bias-dependent Pockels effect.