Multi-stratum factorial designs are quite common in scientific and industrial investigations; a simple example is the so-called split-plot design. Multiple sources of errors with different variances, called strata, arise from complicated structures of the experimental units. Despite plenty of applications, most relevant research in the literature is built on a case-by-case basis even though a general and elegant theory of multi-stratum factorial design has been well-developed for half a century. This theory is to be introduced in this talk. Several criteria for selecting multi-stratum factorial designs, including those up-to-date, are presented and discussed.