Currently, the most popular alternative to the CRT is the Liquid Crystal Display (LCD). LCDs are organic molecules that, in the absence of external forces, tend to align themselves in crystalline structures. But, when an external force is applied they will rearrange themselves as if they were a liquid. Some liquid crystals respond to heat (i.e. mood rings), others respond to electromagnetic forces.
When used as optical (light) modulators LCDs change polarization rather than transparency (at least this is true for the most popular type of LCD called Super-twisted Nematic Liquid crystals). In their unexcited or crystalline state the LCDs rotate the polarization of light by 90 degrees. In the presence of an electric field, LCDs the small electrostatic charges of the molecules align with the impinging E field.
The LCD's transition between crystalline and liquid states is a slow process. This has both good and bad side effects. LCDs, like phosphors, remain "on" for some time after the E field is applied. Thus the image is persistent like a CRT's, but this lasts just until the crystals can realign themselves, thus they must be constantly refreshed, again, like a CRT.