On the way to work yesterday I could smell burning rubber and then the the battery light came on on my dashboard. I took a look under the bonnet and noticed that my fan belt had disappeared. (The fan belt doesn’t actually drive the fan, but the terminology remains from old engines where it would have done).
The fan belt actually drives the alternator which charges the cars battery, so without it eventually your car electrics will drain the battery, your headlights will get dim, you will probably get some misfiring and the car will stop working, possibly leaving you without even hazard lights. Therefore replace it immediately.
You would get the same symptoms (battery light, dim headlights, misfiring) if the alternator has become disconnected, blown a fuse or just expired.