Hypersurfaces are subvarieties whose codimension is one. This makes their study a little easier because the structure equations are simpler. Within the family of symmetric spaces, the most prominent are those of rank 1, i.e. Euclidean, spherical, hyperbolic, their complex analogues and quaternionic. In recent years the focus has moved to some rank 2 symmetric spaces, such as the complex quadric and the Grassmannians. This field has been very fruitful, with almost a thousand publications in the last 50 years. Usually, an attempt is made to classify those hypersurfaces that satisfy certain tensor cut-off equations, usually referring to the Weingarten endomorphism and the curvature and Ricci tensors.