Just Electrostatic speakers, or panel speakers that use other technologies like Ribbon and Planar?
Both have similar pro's and cons.
Electrostatics usually have quite low dips in the mid-treble impedance so need an amplifier that does not mind that, but they are relatively benign at low frequencies. They also require a power cable to energise the electrostatic panel.
An example of the Electrostatic speaker are the Quad speakers, like the ESL-57, 63 and the newer models. Martin Logan have Electrostatic mid-treble and hybrid dynamic cone active bass in most of their models, and some of their high end use Electrostatic bass panels I believe.
Some others are Kingsound, B&W made a hybrid back in the 70's and a few others.
Panel speakers like ribbons, or planar tend to have a purely flat and resistive impedance, thus making them very easy to drive, although usually at low impedance (4 Ohms) and are quite in-sensitive so require a lot of power. They do not require mains power to the speaker.
Magnepan uses both Planar technologies (bass panels in all their speakers, and hybrid treble in the MMG) and then Ribbon tweeters in the higher end models. This is the same configuration as the Apogee speakers.
Both types have advantages in that the whole panels are energised, so you have a line source that moves the air, resulting in a very large and quite lifelike soundstage. As most, if not all are dipole speakers which means they radiate to the font and back in a figure of 8 pattern. This means that bass acutallu cancels it self out at the sides of the panels, which means they can be placed near to side walls. They need a reasonable amount of space behind them as the the bass-mid-treble are radiated both ways so can muddle up the sound.
Both types also have limited vertical dispersion, the curved panels of the Quad ESL-57 help with this.
I am sure others will add more, thats just all I can think off at the moment.