The complexity of the highly dynamical atmospheric layers of the Sun in the presence of inhomogeneous magnetic fields makes it challenging to correctly interpret observations from space and ground-based instruments. In particular, the center-to-limb variations of spectro-polarimetric properties may lead to significant misinterpretations of helioseismic and magnetic observables. To address these challenges and study the physical processes behind observations of various types, we use 3D MHD radiative models, which reproduce the dynamics and observational properties with high-degree realism. To study the center-to-limb effects, we obtained series of synthetic spectropolarimetric and intensity imaging data that mimic observations from different space instruments: HMI and AIA (SDO), SOT (Hinode), and IRIS, as well as upcoming DKIST ground observations. In the presentation, we discuss the influence of observations at different angular distances from the solar disk center on the resulting properties of the magnetic field, atmospheric structure and dynamics, and acoustic and surface gravity waves.