A compzine - coined by contracting compilation and zine - is a zine comprised of pieces written by more than one zinester. Compzines are usually themed, such as featuring pieces by zinesters from the same town, or pieces on the same subject (ie, food, ethics, first sexual experiences, etc).
A typical compzine has one editor who chooses the theme and then sends out submission calls in the form of flyers, letters and/or posts on online zine communities. The editor then compiles the submissions she/he receives and prints the compzine.
Contributors are usually listed in the front or back of the zine, with their contact info, and typically receive a free copy of the zine when it's completed.