My talk is divided in two parts. In the first part I will offer an overview over some of my findings in three-way component analysis, which is the topic that I focused on during my Ph.D. In particular, I will present some results revolving around the issues of simplicity and optimizing the search for global minima. The second part of my talk will focus on research within item response theory (IRT), which is the field where I have being working on in the last years. I will introduce the nuts and bolts of IRT, as well as some results based on person-fit analysis, which provides a means of detecting atypical response patterns of tests or questionnaires.