In ferroelectric materials, the properties such as Curie temperature, polarization switching and ferroelectric domain patterns, are very sensitive to the electrical, mechanical and chemical boundary conditions. This is particularly true at the nanoscale where minimization of the depolarization field drives the formation of new polarization patterns, including whirling ones. In this work, we explore the ferroelectric properties of epitaxial BaTiO3 nanostructures on silicon, with the objective to understand the effect of lateral scaling (< 500 nm) on ferroelectricity and to define routes to stabilize polar textures. The research begins with the investigation of He and Ne focused ion beam milling to fabricate BaTiO3 nanopillars with sub-500 nm diameters from single-crystalline BaTiO3. While He ion irradiation induces surface swelling and blistering due to He nanobubble formation, Ne ion milling proves to be a highly effective method to fabricate BaTiO3 nanopillars. They consist of a defect-free single-crystalline core surrounded on the top and lateral sidewalls by a defect-rich crystalline region and an outer Ne-implanted amorphous shell. We demonstrate that the geometry and beam-induced damage of the nanopillars can be precisely controlled via patterning parameters, establishing Ne ion milling as a useful technique for the rapid prototyping of crystalline nanostructures. Second, we investigate ferroelectricity in 20 nm-thick single-crystalline BaTiO3 nanodisks with diameters ranging from 400 nm down to 100 nm, fabricated using Ne ion milling from a 20 nm-thick epitaxial BaTiO3 film grown on SrTiO3-buffered silicon. The nanodisks are ferroelectric, with a Curie temperature ranging between 230 and 270 °C. Decreasing the diameter leads to an increased amount of Pup polarization relatively to Pdown. Signatures of polar textures emerge in the 100 nm nanodisks in both the lateral and vertical directions. Three distinct configurations are observed for the out-of-plane polarization patterns, consistent with existing theoretical predictions. The up-oriented polarization component can be progressively switched to a down-oriented state using electrical pulses. Third, we present the realization of chiral topological polar states in BaTiO3 nanostructures on silicon. The single crystalline nanoislands, grown by molecular beam epitaxy, are embedded in a continuous 20 nm-thick BaTiO3 layer on SrTiO3-buffered silicon and have a trapezoidal shape with lateral dimensions as small as 30-60 nm. They exhibit a center down-convergent polarization pattern with a swirling lateral component, which confers chirality. The center down-convergent pattern can be electrically switched to a center up-divergent one, occasionally passing through metastable states as experimentally observed and predicted in theoretical simulation. Engineering the shape of nanostructures (a trapezoidal shape similar to a narrowing funnel) is an original and highly promising route to design chiral polar textures. Finally, we investigate optical switching and domain modification in epitaxial BaTiO3 thin films on silicon. The as-grown films contains both a-domains (with in-plane polarization) and c-domains (with out-of-plane polarization). Upon UV laser irradiation (325 nm), ferroelastic and ferroelectric switchings occur leading to a mostly Pup single polarization orientation. Major structural changes are observed, which involve defect motions and full strain relaxation to bulk c-axis BaTiO3. We propose that this structural transformation and the resulting Pup domain configuration are triggered by high strain/stress fields resulting from internal electric fields created by the spatial separation of the photoexcited carriers and by internal heating. Our findings advance the understanding of nanoscale ferroelectrics on silicon, particularly in epitaxial BaTiO3 nanostructures and brings new perspectives particularly for the realization of chiral polar textures. By investigating the effects of lateral miniaturization on ferroelectricity and exploring both electrical and optical stimuli for domain control, this thesis highlights the potential of BaTiO3-based nanostructures for nanoelectronic applications in CMOS technology.