Summarize:

If wisdom teeth fully erupt (come in) through the gums straight, well-spaced and positioned properly in relation to other teeth, then they often cause no pain or inflammation and don't need to be removed. It's only when they partially erupt, lack enough space, grow crooked and/or get infected that they become problematic and noticeable.  Wisdom teeth don't fully erupt in everyone. Sometimes they remain completely hidden within the gums and bone, or they may only partially erupt. The American Dental Association recommends that people between 16–19 years old get their wisdom teeth evaluated by a dentist.  The longer your wisdom teeth stay in your mouth after the age of 18, the more developed the roots become, making them more difficult to remove if they are problematic. Even wisdom teeth that erupt normally through your gums can cause mild symptoms. Look for mild pain, a feeling of pressure, or dull throbbing in the gums near the opening of your throat or in the nearby jaw bone. Erupting teeth can irritate the sensitive tissues that make up your gums (called gingiva). The pain will be more severe if the wisdom teeth are crowded and grow crookedly — they can cut into delicate gum tissues. Pain is subjective — mild pain for some, might be intolerable for others. The point is, some pain can be entirely normal for erupting wisdom teeth, so give it some time (at least a few days) before seeing your dentist.  Eruption of wisdom teeth is not continuous, so every three to five months you may experience the same pain for a few days. The wisdom tooth eruption influences the bone position of the other teeth so you may find that your teeth begin to shift. If the wisdom teeth are not able to erupt normally, they may become trapped or impacted within your jawbone. This increases the risk of infection (see below). The pain from erupting wisdom teeth can get worse at night if you have a habit of clenching your jaw and/or grinding your molars. Chewing gum may also aggravate the pain caused by wisdom teeth. While the pain typically goes away without professional intervention, there are a variety of ways to help ease the pain for you to try in the meantime. Wisdom teeth can also trigger redness and swelling (inflammation) in the gingiva. You may be able to feel the swollen gums with your tongue. They make it more difficult or uncomfortable to chew food while inflamed. Take a small penlight and shine it into your mouth while looking in a mirror. Wisdom teeth are the very last teeth (most posterior) in each row. Look for the top of the teeth (cusps or crown) poking through the gums and see if the tissue looks redder or swollen (called gingivitis) than other areas. The swelling usually goes away after a week or so.  While looking in your mouth, you might see some blood around the protruding wisdom tooth, or your saliva may be tinged red. This is relatively uncommon, but not rare. Other causes of blood can include gum disease, canker sores or mouth trauma. You might see a "gum flap" over your erupting wisdom tooth, which is known as a pericoronal flap. This is normal and doesn't usually cause any problems. While your rear gum tissue (gingiva) is swollen, it might be difficult to open your mouth. You may need to drink fluids through a straw for a few days. You may also find it difficult to swallow. Your dentist may prescribe some anti-inflammatory medication for you to take for a few days. Lower wisdom teeth are close to your tonsils, which may swell, giving you the feeling of getting a cold or sore throat.
Don't always expect symptoms. Look out for gum or jaw pain. Watch for redness and swelling.