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We give an expository review of applications of computational algebraicstatistics to design and analysis of fractional factorial experiments based onour recent works. For the purpose of design, the techniques of Gr\"obner basesand indicator functions allow us to treat fractional factorial designs withoutdistinction between regular designs and non-regular designs. For the purpose ofanalysis of data from fractional factorial designs, the techniques of Markovbases allow us to handle discrete observations. Thus the approach ofcomputational algebraic statistics greatly enlarges the scope of fractionalfactorial designs.

Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics