Factorial designs are the most common type of experimental design. In a factorial design several factors are controlled at two or more levels, and the effect on the response is investigated.
There are two main types: Full Factorial Designs and Fractional Factorial Designs. In Fractional Factorial designs the amount of testing is reduced, but the downside is that some interactions and factors are aliased. One of the limitations of Fractional Factorial designs is that the number of runs is 2n, if there are more than a few factors this leads to large gaps in the available options (4, 8, 16, 32, 64, 128, etc.). Plackett-Burman designs overcome this, but at the expense of confounding. Other approaches to the Design of Experiments include Response Surface Methods and Taguchi Designs.