I’m going to focus on the applications that any trained martial artist with a little weapons training can execute, beginning with the finishing moves. Bamboo wushu fans are more than sufficient.
- Striking with the butt of the fan into the solar plexus or kidneys
These strikes are very similar to how one uses a kubotan, and can end a conflict if applied well. Essentially, the fan is closed, the wielder has left about an inch of space between the bottom of the palm and butt of the weapon. This techniques can also be used to strike the temple.
- Thrusting the closed fan into the throat
This is obviously a potentially fatal strike if executed with sufficient force, damaging the trachea, so use caution. This can be applied even with very little training, due to the shortness and lightness of a bamboo fan, compared to the skill required for sword or spear.
This was a great answer by LazyReader, "wrist bone or between the ulna and radius, near pressure points" and I will only elaborate that it should be effective against a knife, because of the number of nerves, which, if applied correctly can cause spasm or loss of feeling. (It also hurts like a [redacted], speaking from personal experience;) Here the bamboo is arguably ideal because of the quickness—metal fans that sometimes appear on the market can be overly heavy, and could even present a disadvantage against a knife for this reason. Bamboo also seems to distribute force in an optimal way to affect the nerves.
- Thrusting into the pelvic joint
I believe it's the periformis muscle and surrounding nerves. Regardless, man is it nasty, and it will definitely cause spasming.
- Striking into the face with the tines of the open fan.
This was another application LazyReader astutely referenced, and I'll only add it's plenty nasty even with a bamboo fan. The bamboo tines are strong enough to break the skin, and, if they make contact with the eyes, cause significant trauma. (Forget a sharp stick in the eye—getting poked with any stick in the eye is terrible, and there's also the possibility that the bamboo breaks and splinters, which could cause puncture wounds.)
- Striking/pushing up under the chin with the open fan
This one gets forgotten, but there is soft tissue under under the chin, glands at the side, and it's not a strike most people will expect. Pushing up this way can force the opponent's head up, which has multiple advantages (potential to unbalance, reduced visibility.)
These are the techniques that require significant training, because they involve opening and using the opened fan in a less direct manner.
This applies to fan with fabric connecting the tines—in the bamboo wushu fans would will notice about an inch of extra fabric at the ends. "Shooting" the fan (snapping it while open) across an opponents eyes will cause them to tear up, and there is also the possibility of cutting the cornea (think paper cuts.)
- Strumming/opening the fan
This is where you snap the fan open, or "strum" it in an in-between state. It's pure distraction and effective b/c it's [redacted] LOUD as [redacted] with a bamboo fan, painful on the eardrums when applied correctly close to the head, and it's unlikely anyone is not startled—even people who are used to it don't enjoy it. One would use this to distract before applying a strike.
- Using the fan to obstruct the vision
This is my favorite, and it was years before I even realized what was going on. Essentially, the wielder can open the fan with the palm downward at a ~45 degree angle so that it blocks opponent's view of the wielder's feet, such that the wielder can connect with a heel kick to the inside of the opposite knee, stomp to the bridge of the foot, or, if being gentle, simply control the opponent's knee with the instep, forcing them to the ground.
[The fan can also be used in joint locks, but these techniques are more complex, and therefore more risky, and require significant training and two person practice. An open fan can indeed also be used to redirect a weapon, but requires significant training, finger strength, and is still quite risky against an edged weapon b/c the fingers are exposed.]