In the present article, the theory of ANOVA-target projection (ANOVA-TP), a method aimed at analyzing multivariate data coming from designed experiments is presented. ANOVA-TP, similarly to ANOVA-principal component analysis (ANOVA-PCA), ANOVA-simultaneous component analysis (ASCA) and other related methods, starts from a multiple ANOVA decomposition of the multivariate experimental data matrix. Partial least squares analysis is then used to relate suitably built effect submatrices to the design terms, and postprocessing by target projection constitutes the basis for interpretation. The proposed approach is illustrated by different examples, showing the versatility of the method in dealing with crossed-factors full factorial designs, repeated-measurement designs and longitudinal studies.