Grouping experimental units by some property unrelated to the treatments can substantially increase precision and power without increasing the sample size. We discuss designs for such blocking, starting from the randomized complete block design up to different designs with replicated Latin squares. We also consider incomplete block designs. We present methods for choosing and evaluating blocking factors and discuss fixed block factors and the interpretation of block-by-treatment interactions. We make extensive use of Hasse diagrams to discuss different variants of blocked designs. We introduce simple linear mixed models as an alternative to analysis of variance, particularly for incomplete block designs.