In live music production, we mostly use just two types of microphones: Dynamic and Condenser. Either can be large or small diaphragm and they vary greatly in sonic quality, depending on the make and model. But the main difference between them are the actual mechanics for converting acoustic sound into electrical signal. I’ll go into more detail in another post.
But there's yet another type of microphone that can be great for live sound, called a Ribbon mic. These have diaphragms that are more fragile than dynamics or condensers, which is part of what gives them their sonic quality. They tend to sound really smooth, with a rich and detailed mid-range. I really love them on electric guitar amps and they're also great for sustained keyboard sounds like organ.
However, since the diaphragm can be fragile, ribbon mics have not traditionally been used much in live sound. It's far easier to protect them in a studio where you don't have a ton of people moving around on stage. A really hard hit or drop can easily put a ribbon mic out of commission, especially a vintage one!
Thankfully, modern microphone design has solved some of these issues and there are options out there that are totally usable for live shows. For example, on tour the past couple of years I've been using a pair of Shure KSM313 ribbon mics for electric guitar. They've been around the world a few times and even done a bunch of outdoor festival gigs with questionable weather. They're still holding strong and sounding great.
Apart from the relative fragility, ribbons do have a couple other aspects that don't make them ideal for live situations. First of all, by design, ribbon mics have a bi-directional polar pattern. This means they'll pick up sound from both the front and back equally. On a loud stage, this isn't really ideal!
The studio is much easier to control and we can get some good isolation with barriers or by careful mic placement. In live sound, however, we're just putting the mics close to the instruments on stage and we can't always get good separation between instruments. Bidirectional mics don't help with this, but if the source is a decent volume, like an electric guitar amp or trumpet, it's usually manageable and worth it for the smooth tone.
An additional concern is phantom power (+48v). Applying this direct current to a ribbon can kill the diaphragm and ruin the mic. Again, some modern designs are more robust and won't be damaged by phantom (a couple models even require +48v to operate). But it's still a concern for most ribbon mics and you have to be careful with this when setting up audio for a show.
In the fast workflow of live sound, it's easy to accidentally apply phantom, drop the mic, or not have the ability to isolate something on stage. So, you probably won't see many ribbons as part of a venue’s mic kit. But within the infrastructure of a touring audio production, where the stage positions, consoles, mics, and cabling are all consistent from show to show, they can be a fantastic tool for getting the perfect tone on certain instruments.