The intracluster medium (ICM) in the centers of galaxy clusters is heavily influenced by the “feedback” from supermassive black holes (SMBHs). Feedback can drive turbulence in the ICM and turbulent dissipation can potentially be an important source of heating. Due to the limited spatial and spectral resolutions of X-ray telescopes, direct observations of turbulence in the hot ICM have been challenging. Recently, we developed a new method to measure turbulence in the ICM using multiphase filaments as tracers. These filaments are ubiquitous in cluster centers and can be observed at very high resolution using optical and radio telescopes. We study the kinematics of the filaments by measuring their velocity structure functions (VSFs) over a wide range of scales in the centers of ∼ 10 galaxy clusters. We find features of the VSFs that correlate with the SMBHs activities, suggesting that SMBHs are the main driver of gas motions in the centers of galaxy clusters. In all systems, the VSF is steeper than the classical Kolmogorov expectation and the slopes vary from system to system. One theoretical explanation is that the VSFs we have measured so far mostly reflect the motion of the driver (jets and bubbles) rather than the cascade of turbulence. We show that in Abell 1795, the VSF of the outer filaments far from the SMBH flattens on small scales to a Kolmogorov slope, suggesting that the cascade is only detectable farther out with the current telescope resolution. The level of turbulent heating computed at small scales is typically an order of magnitude lower than that estimated at the driving scale. Even though SMBH feedback heavily influences the kinematics of the ICM in cluster centers, the level of turbulence it drives is rather low, and turbulent heating can only offset ≲ 10% of the cooling loss, consistent with the findings of numerical simulations.