Recent observations suggest that accretion streamers are common in protoplanetary disks, yet their dynamical impact on disk evolution remains poorly understood. Using three-dimensional hydrodynamic simulations with mass infall rates of 10⁻⁸--10⁻⁶ M_⊙ yr⁻¹, we investigate how streamer accretion influences the structure and evolution of protoplanetary disks. We find that a prograde streamer can excite disk eccentricity globally to values as high as ∼0.4. The resulting eccentric disk develops prominent spiral arms and crescent-shaped overdensities whose spatial structures agree remarkably well with analytic eccentric-disk theory. It also undergoes significant warping, and exhibits enhanced and variable stellar accretion. In contrast, retrograde streamer accretion efficiently removes disk angular momentum, producing a compact disk and, in extreme cases, triggering disk breaking. Using synthetic ALMA molecular-line observations, we show that streamer-driven perturbations generate observable kinematic signatures, including Doppler flips in moment maps and wiggles in position–velocity diagrams. Remarkably, these signatures can persist for up to 100 kyr after infall has ceased, suggesting that some kinematic disturbances observed in disks without currently detected streamers may be relics of past infall events. Finally, we discuss the implications of streamer-driven disk evolution for planet formation and planet–disk interactions.