In this chapter we give a discussion of projective submanifolds in general, and revisit a few examples (quadrics, in particular) that are important for a number of different reasons. We use thee technique of moving frames a la Elie Cartan. This technique is effective in uncovering various degeneracy phenomena as regards projective subvarieties. Thus the material in the chapter is somewhat separate from the rest of the book; nevertheless serves to provide a context of sort. The main reference for this chapter is the article [Griffiths-Harris2]. See also [Yangl], where the metric geometry of projective submanifolds is discussed.