This chapter is concerned with the theory of the design of filters using resonators which are constructed using low loss high permittivity ceramics. Initially the fundamentals of modes in dielectric rod waveguides are discussed. An example of a filter using these resonators is presented. Next a discussion of dual-mode in-line dielectric filters is followed by details of the design of dual-mode conductor-loaded dielectric resonators. These find application in cellular radio base stations and a design example is presented. The use of triple-mode resonators enables significant size reduction compared with single-mode designs. The exact theoretical modelling of triple-mode spherical dielectric resonators is described. This is followed by the design theory and an example of a triple-mode reflection filter. Finally the use of dielectrics for extreme miniaturisation by loading TEM and waveguide structures is discussed.