Ferroelectric materials are characterized by the presence of spontaneous polarization that can be reoriented under a sufficiently high electrical field. The couplings between ferroelectric polarization with external fields, such as temperature, mechanical stress, electrical fields, and magnetic fields, enable a multitude of applications, including pyroelectric detectors, ultrasonic transducers, energy storage capacitors, and nonvolatile random-access memories. The electromechanical coupling is particularly strong in ferroelectric materials and can manifest itself in two aspects. The primary electromechanical effect is the piezoelectricity, which describes the coupling between stress/strain and polarization/electric fields. A less well-examined electromechanical interaction is the flexoelectric effect, which associates polarization with strain gradients and mechanical stress with electric field gradients. This dissertation is about these two electromechanical coupling effects in ferroelectric materials. The dissertation is motivated by two electromechanical phenomena that have been revealed recently in ferroelectric materials at distinct length scales, namely, the AC poling effect and the mechanical switching. The first phenomenon refers to the considerable enhancement of the piezoelectric coefficient of a bulk relaxor-ferroelectric crystal by poling the crystal with alternative current (AC) electric fields compared to that poled with commonly used direct current (DC) electric fields. The second phenomenon describes the mechanically induced 180-degree polarization switching at the nanoscale by pressing an atomic force microscopy (AFM) tip onto a ferroelectric epitaxial thin film. The goal of the dissertation is to reveal and understand the primary mechanisms that govern these electromechanical phenomena by phase-field modeling and simulations and utilize the gained knowledge to guide the design of advanced materials for high-performance transduction applications and novel nonvolatile memories. The main content of the dissertation consists of two parts. In the first part, the AC poling effect on the piezoelectricity of bulk single crystals is investigated. First, the general domain size effect on the piezoelectricity of a bulk ferroelectric crystal is examined by evaluating the effective longitudinal piezoelectric coefficient of a polydomain twin structure with a varied domain size using the phase-field method and thermodynamic calculations. In contrast to the common belief that a smaller domain size always favors higher piezoelectricity, we show that the domain size effect is by no means universal; it depends on the symmetry of ferroelectric phases, types of domain walls, temperatures, external electric fields, mechanical stress, and probing directions. Moreover, the domain size effect becomes more significant in the proximity of a phase transition, regardless of the nature of the phase transition. Essentially, the domain size effect is attributed to the polarization rotation in the domain interior due to the presence of domain walls, which can give rise to either the positive domain size effect (smaller domain, higher piezoelectricity) when the polarization rotation is associated with a phase instability or the negative effect (larger domain, higher piezoelectricity) when such an instability is absent. These understandings offer new insights for the processing-microstructure-property relationship and the concept of domain engineering in piezoelectric single crystals. Next, the evolution of domain structures in relaxor-PT single crystals under AC- and DC-electric field poling is investigated by phase-field simulations in order to reveal the mechanism of AC-poling effect on the domain structure and piezoelectricity. Taking (001)-oriented rhombohedral Pb(Mg1/3Nb2/3)O3-28PbTiO3 as a model system, we find that both DC- and AC-poling can increase the domain size of the unpoled crystal and form the engineered domain structure with a lamellar configuration. However, the AC poling allows for further domain growth via the elimination of tilted 71° domain walls during the cycling of the electric field, which finally leads to a layered structure with a set of single domains separated by horizontal 109° domain walls. In contrast, the DC-poled crystal is abundant with both types of domain walls. It is also predicted that the decrease of 71° domain wall density is responsible for the enhanced longitudinal piezoelectric coefficient in AC-poled crystals. Both aspects of our theoretical findings have been corroborated by experiments. Moreover, the AC-poled crystal with the unique layered domain structure simultaneously exhibits nearly perfect optical transparency and significantly improved light transmittance, birefringence, and electro-optical coefficient aside from ultrahigh piezoelectricity. This transparent crystal with ultrahigh piezoelectricity by design will benefit hybrid opto-electromechanical applications such as photoacoustic imaging and haptic devices. The second part of the dissertation focuses on discussing the role of flexoelectricity in the mechanical switching of local polarization in ferroelectric thin films by AFM tip pressing. The mechanical switching phenomenon is investigated in (001)-oriented uniaxial tetragonal BaTiO3 thin films and multiaxial rhombohedral BiFeO3 epitaxial thin films. In BaTiO3 thin films, we systematically evaluate the critical force F_c required for the polarization reversal as functions of the AFM tip radius, misfit strain, and film thickness by performing phase-field simulations and compare our results with experiments where available. The deviations between simulation and experimental results on the film thickness dependence of F_c is elucidated by examining the misfit strain relaxation and the surface polarization relaxation. In particular, we reveal an interplay between the flexoelectric and piezoelectric effects during a loading-unloading cycle of mechanical switching. This work provides a deeper understanding of the mechanism and control of mechanically induced ferroelectric switching and thus guidance for exploring potential ferroelectric-based nanodevices utilizing mechanical switching. The mechanical switching mediated by the flexoelectric effect is limited by its unidirectional nature of the tip-induced flexoelectric field. As a result, local polarization can only be switched from upward to downward but not the opposite. A strategy is proposed to circumvent this limitation based on phase-field simulations of the mechanical switching in multiaxial BiFeO3 thin films where both out-of-plane and in-plane polarization can be reversed. Specifically, it is found that the in-plane flexoelectric field can be asymmetrically enhanced by the motion of a scanning AFM tip. By controlling the tip scan direction, one can deterministically select either stable 71° ferroelastic switching or 180° ferroelectric switching. Further examinations reveal an interplay between piezoelectric and flexoelectric effects in enabling such a selective polarization switching. This work opens a new avenue for the deterministic selection of nanoscale ferroelectric domains in low-symmetry materials for nonvolatile magnetoelectric devices and multilevel data storage.