We discuss the theory of quasi-static coronal loops, introducing a phase plane representation to study loop solutions independently of specific boundary conditions. Emphasis is put on the effects of loop expansion, heat input and gravitational stratification on the differential emission measure, and on the intrinsic limitations of spectroscopic observations for deriving loop parameters. We show that certain classes of published loop solutions cannot actually exist. For expanding loops new classes of loop solutions, with rather special properties, are presented. Special attention is paid to loops in binary systems and on rapidly rotating stars.