As far as penises go, when erect, they all have some degree of curvature, but it is much more pronounced in some men than others.
Naturally, an erect penis may have a slight curve because of the different chambers that make up the penis. There is one corpus spongiosum, that surrounds the urethra and is found on the underside of the penis up to and including the glans (head). Then there are two corpus cavernosa on the left and the right side of the top of the penis (at a position parallel to the ground). If either of these two chambers are longer than the other, then an erection may bend slightly to the left or to the right. If the two corpus cavernosa are shorter than the corpus spongiusum below the glans, the erection may bend slightly upwards.
Usually, a slight curvature of the penis on erection is normal and to be expected. It may be simply from anatomical development, or years of placing the penis on one side or the other in your underwear. Just the simple act of adjusting it to one side several times a day may gently stretch the connective tissue of the penis so that one side is longer than the other. Normally, a gentle curve does not cause any difficulties or interfere with sexual activity. Some men, however, experience a much more dramatic curvature that can be problematic. Such is the case with Peyronie's Disease.
Peyronie's Disease is a condition that forms in the penis as a result of increased scar tissue that forms on the tunica albuginea (connective tissue) on one side of the penis. Because this scar is not elastic like the other connective tissue found in the penis, it stays the same length while other tissues in the penis expand during an erection. Because the scar tissue stays the same length, the rest of the erection needs to bend around it, forming a very pronounced curve. Sometimes the angle of curvature is so severe that it becomes difficult just to have penetration. Other men experience pain with an erection, and some find it difficult to keep an erection because they have venous leakage due to poor tension when the start to get an erection.
It is believed that Peyronie's can develop in a man in response to trauma to the penis, or even microtrauma with miniscule tears of the tunica albuginea (the connective tissues that surround the erectile tissue). In an attempts to heal this trauma/microtrauma, the body lays down scar tissue to seal it up. Often, there is nothing out of the ordinary that a man has done to cause this, and it may be that some men are more genetically predisposed to this scar tissue formation than others, as evidenced by the fact that up to 20% of these men have scar tissue development in other parts of their body as well. In Peyronie's, there is an active phase of the disease when the body is actively forming more scar tissue, and an inactive phase where the scar tissue is relatively stable. Sometimes, a man may have scar tissue formation that improves on its own without treatment, but other times, treatment is required to resolve this.If a man does develop Peyronie's Disease, there are a few treatment options. Since there can be resolution of the plaque on its own, treatment is recommended to be done during the inactive phase of the disease. There are medication options that may reduce the scar tissue, such as Vitamin E or other medications taken orally. Other medications that help dissolve the scar plaque can be injected directly into the plaque to try to break down the scar tissue itself. If medications have not improved a severe curvature, there are several surgical techniques that a urologist could try. Normally, medications are tried for at least a year before taking a more invasive approach. Studies have also found that use of mechanical penile extenders can also help some men, but these can be uncomfortable and are usually worn for 5 hours or more per day for 6 months to a year. This method stretches the scar tissue over time, but should be done carefully and under the supervision of an urologist to ensure there is no repeated injury to the penis and more scar formation.