We consider reflection of electromagnetic waves from layered structures with various dielectric and magnetic properties, including metamaterials. Assuming periodic variations in the permittivity, we find that the reflection is in general anomalous. In particular, we note that the specular reflection vanishes and that the incident energy is totally reflected in the backward direction, when the conditions for resonant excitation of leaking surface waves are fulfilled. [1,2,3,4,5,6,7,8,9,10], it is necessary to reconsider many well known problems, accounting also for metamaterials. Due to their extraordinary properties, lefthanded materials are believed to become highly important in various technological applications [1,2]. The first examples of metamaterials had their left-handed properties in the microwave range, and then later for infrared waves [11]. Recently materials showing anomalous refractive behaviour have been constructed also in the optical regime [2].It has previously been shown in Ref.[12] that certain layered dielectric structures give rise to peculiar reflection phenomena, provided surface waves [7,8,13,14,15] can be excited. Such waves have previously been considered in connection with layered structures [9,10,12,16], open plasma wave guides [17,18], and fusion plasmas [19].In the present paper, we consider the reflective properties of a dielectric and magnetic medium with arbitrary permittivity and permeability, which is covered by a dielectric layer. We show that for a homogeneous medium, we have the familiar specular reflection independently of the material parameters. However, with periodic variations in the dielectric permittivity, as can be found in nature [20,21] and constructed in laboratories [1, 2, 11], we find that the incident energy can be completely converted into a backscattered energy flux, a phenomenon which is associated with the resonant excitation of leaking surface waves. The necessary conditions for obtaining backward reflection will be deduced, and possible applications of this peculiar mirror effect are consequently pointed out.Homogeneous media We first consider a semi-infinite (z > z 0 , region a) material with arbitrary relative permittivity ε a and permeability µ a . Specifically we will allow these constants to have arbitrary signs, such that for example metamaterials with negative signs of both ε and µ are included as special cases. This material is assumed to be covered by a dielectric layer with arbitrary permittivity ε b and µ b = 1 in the region 0 < z < z 0 (region b), whereas we have vacuum at z < 0. Fur-