We present fractional factorial designs for multiple treatment factors on two levels, where effects are deliberately confounded to reduce the experiment size. Such a design can be defined by one or more generators, which formally describe the confounding, and simple algebraic manipulations of these generators allow for the derivation of all effect aliases in the design. We discuss using fractional factorials with blocks, and we show how multiple generators can then be used to disentangle confounded effects. Screening experiments are an important application of fractional factorial designs; we also introduce Plackett-Burman designs for this purpose.