Punches can place serious force against your elbows at odd angles.
Boxing isn't called the "Sweet Science" for nothing. As brutal as the sport can sometimes be, it takes a rare blend of athleticism, fitness and finesse to throw punching combinations with speed and power. Because boxing combinations are so powerful, you need to make sure your joints are strong enough to handle the rigors of training. Without a strong elbow joint and tendons that surround it, you won't be hanging around the sport for long.
Perhaps the most important exercise for any boxer is that of shadow boxing. Shadow boxing involves throwing loose, fast punching combinations into thin air with nothing but your own imagination as an opponent. Elbow injuries can occur when you overextend on punches, so learning to retract punches with as much speed as you throw them can condition your elbows to the effects of a fast punching combo. Shadow boxing also allows you to strengthen your elbows without applying force to the joints.
Once you've gained comfort throwing punches from various angles and at high speeds, you need to ramp up your training by throwing them against bags. Punching bags come in many shapes and sizes, from densely-packed heavy bags to light speed bags. Start out light on the bags before ramping up the power and intensity over time. Conditioning your elbows to the recoil impact of striking a target will make them more resistant to injury.
As is the case with any complex joint, elbow injuries can range from minor to acute. Boxing injuries of the acute variety could include elbow dislocations, tendon tears and serious damage to the structures around the elbow. These injuries require medical attention and possibly surgery. For minor injuries overuse and boxer's elbow, which involve pain in the posterior of the joint, rest and rehabilitation should be sufficient.
Once you damage your elbows by striking too hard and too fast or missing the target completely, you need to take a patient approach to make a full and lasting recovery. Strengthening exercises include liberal stretching of the area, along with exercises to strengthen the grip. Working on wrist flexion will help to strengthen tendons that run from the hand all the way up to the elbow. Working directly on the elbow joint may be too aggressive and could further aggravate the injury.