Chemical peels use a combination of acids ranging from extremely mild to acids strong enough to produce second degree burns of the skin. The combination of acids is chosen depending on the problems that the peel is intended to address. The stronger the peel, the deeper the penetration, and the higher likelihood of side effects associated with the peel. As with all peels, proper follow up care is required to reduce the likelihood of infection and other problems.
The mildest of peels, the superficial peel is the least aggressive and as such carries fewer side effects than the deeper peels. Removing only the epidermis, the outermost layer of the skin, you can expect mild redness and peeling to occur.
Medium peels are more aggressive than superficial peels and are intended to penetrate to the upper portion of the dermis. The peel ‘wounds’ the skin by causing a second degree burn which allows the skin to heal and rejuvenate itself. With this peel you can expect scabbing, redness, peeling, flaking, and swelling. In some cases hypopigmentation, lightening of the skin, may occur.
In the case of deep peels involving Phenol there have been cases of cardiac arrest and even death which is why these peels are generally performed in a hospital setting under anesthesia. 
General side effects include pain, extreme redness, swelling, scabbing, peeling, flaking, hypopigmentation.
 ” Chemical Peels | DERMAdoctor.” Dermatologist recommended skin care products and skin health information. | DERMAdoctor. N.p., n.d. Web. 21 Apr. 2011. <http://www.dermadoctor.com/article_Chemical-Peels_140.html>.