Achieving ultrahigh-speed electro-optic modulators (subterahertz modulation bandwidths) is shown to be feasible in the thin-film lithium niobate integrated photonic platform. Design guidelines for optimization of the main radio-frequency and optical parameters are presented, and 3-dB modulation bandwidth up to 400 GHz is proved attainable in 3-mm-long devices. Such unprecedented bandwidths pave the path towards utilizing the devices in advanced optical communication systems.