Spin-orbit coupling (SOC) intrinsically couples the internal spin degrees of freedom of atoms with their center-of-mass motion and profoundly shapes the single-particle dispersion, providing a highly controllable platform for exploring unconventional quantum phases in ultracold gases. Unlike intrinsic SOC in condensed-matter systems, synthetic SOC in ultracold atoms can be engineered through atom-light interactions. This review summarizes recent progress in spin-orbit-coupled Bose-Einstein condensates (SOC-BECs) with a distinct focus on interaction effects. We systematically discuss how short-range and long-range interactions affect the ground-state structures, low-energy excitations, superfluid properties, and dynamical responses of SOC-BECs, while also considering the roles of quantum fluctuations, finite temperature, and finite-size effects. We first outline the realization of synthetic SOC and its impact on single-particle dispersion. In onedimensional Raman-induced SOC systems, the lower dressed band can develop two degenerate minima at finite momenta, providing the basis for interaction-driven many-body phases. Short-range contact interactions dictate the occupation and coherent superposition of these minima, driving quantum phase transitions among stripe, plane-wave, and zero-momentum phases. Their characteristic signatures include anisotropic sound propagation, roton-like softening at finite momentum, modified collective modes, and anisotropic superfluid responses. We also discuss how quantum fluctuations, finite temperature and finitesize effects modify the ideal zero-temperature mean-field phase diagram, such as phase boundaries and experimentally observable responses. We then examine SOC-BECs with long-range interactions, focusing on dipole-dipole and Rydbergdressed soft-core interactions. Their nonlocal character makes the system energy dependent on the relative arrangement of different spatial regions, leading to spatial density modulation, self-organized structures, spin textures, and topological configurations. In dipolar systems, quantum fluctuations can provide an additional stabilization mechanism for quantum droplets and supersolid structures, while recent studies of two-dimensional dipolar SOC-BECs have revealed topological supersolid states involving meron-like and skyrmion-like spin textures. These developments can be understood within a common physical picture in which SOC reshapes the single-particle dispersion, while interactions and quantum fluctuations jointly determine the ground-state structure, stability, excitation properties, and dynamical behaviour. A central perspective of this review is that periodic density modulation alone is insuffcient to establish genuine supersolidity. Reliable identification requires combining static density and coherence measurements with low-energy excitation spectra, structure factors, collective responses, superfluid observables, and nonequilibrium dynamics. Finally, we outline future directions, highlighting the need to explore higher-dimensional SOC platforms and investigate finite-temperature dynamics. Crucially, future efforts must bridge the quantitative gap between theoretical predictions and experimentally accessible dynamical observables.