Using numerical calculations, we present the design of terahertz transmission modulators based on transmissive metal–insulator–metal metasurfaces, which consist of two planar arrays of parallel metallic ribbons while the deeply-subwavelength space between them is infiltrated with nematic liquid crystals (LCs). We demonstrate that only metasurfaces with narrow lateral gaps between adjacent metallic ribbons have a single transmission peak and low background transmission. Spectral shifting of the transmission peak is then provided by the electrical control of the LC refractive index. The proposed modulators operate either as spectrally-tunable passband filters in a certain frequency range or as amplitude (transmission) modulators at a single specified frequency. Optimal modulators have the following properties: maximal relative spectral shift of around 10%, transmittance change of around 0.6, modulation depth …