There are five ways to remove paint from a brick wall: sandblasting, a heat gun, a peel away gel/paste, a regular paint stripper or environmentally friendly strippers like Soy Gel or Citristrip. Brick walls that have been painted before 1970 may contain lead, so it is best to use a method that allows for containment of the paint as it is removed from the brick.
The sandblasting method is by far the easiest and quickest way to remove paint from a brick wall. However, this method may damage the brick in the process. In addition, clay bricks are created to have a tough outer "shell" that may be severely damaged or completely removed if sandblasted, which will lead to increased deterioration of the brick.
A heat gun is beneficial in that it may be used over and over once it has been purchased and is relatively cheap, between $50 and $120. However, the gun is only to be used on one small portion of the wall at a time and may not fully succeed in removing the paint from brick that is exceptionally porous.
A peel-away gel/paste is good in that it strips and contains the paint to a piece of fabric or special covering paper during the removal process. Regular paint stripper is also a quality product that will remove paint effectively. However, there are harmful effects if the product comes in contact with the skin, in addition to environmental concerns when it is washed from the brick itself. The Citristrip and Soy Gel strippers may not remove the paint as effectively as the peel-away or paint stripper. However, it is safer to use on the bricks themselves, with less harm done to the environment.