Graphene is a perfect infinite single layer of sp2-bonded carbon atoms densely packed into a benzene-ring structure. The confinement of electrons in two dimensions and the peculiar symmetry of the carbon network give graphene exceptional electronic properties that make it a promising material for carbon-based nanoelectronics and spintronics. In particular, the performances of such devices rely on the exceptional intrinsic carrier mobility of graphene. However, extrinsic scattering sources due to standard SiO2 substrates limit the mobility. Hence, the quest for alternative substrates is mandatory in order to increase the mobility beyond the extrinsic limits.Among the possible candidates, ferroelectric (FE) substrates are the most promising due to their ultrahigh dielectric constant and hysteretic dielectric response to an electric field (Objective 1). In addition, periodic polarization domains can be written in FE materials, resulting in a substrate with tunable periodic potential that would allow the engineering of the electronic properties of graphene without etching (Objective 2). Further, a magnetic FE (magnetoelectric, ME) substrate can induce magnetism in graphene and can transfer the ME properties to the graphene itself, hence allowing for electrical control of magnetism in graphene (Objective 3).The three Objectives of the present Proposal concern the theoretical investigation of these new hybrid graphene-FE and graphene-ME systems. Unveiling the properties of graphene-FE and graphene-ME interfaces is a fundamentally important first step towards the development of novel nanoelectronic and spintronic devices. In order to achieve the accuracy needed to capture the fine physical details and due to the nanoscopic scale of the systems to be studied, quantum-mechanical computations with atomic resolution are necessary. Hence, first-principles techniques based on Density Functional Theory (DFT) are the method chosen to address the proposed objectives.