In this thesis metamaterial radar absorbers and plasmonic structures have been investigated. Following a brief overview covering metamaterial structures, and their applications in various areas of Microwave Engineering, a novel thin metamaterial wideband radar absorber, formed by two layers of resistive Hilbert curve arrays, is proposed and analysed numerically in HFSS, revealing a reduction in Monostatic Radar Cross Section (RCS) of more than 10 dB from 9.1 to 18.8 GHz (70% fractional bandwidth) for both polarizations. The structure has thickness of only 0.11Gamma to 0.24Gamma at lowest and highest frequencies respectively. The lateral dimensions are only 0.13Gamma to 0.3Gamma per unit cell at lowest and highest frequencies respectively which is several times smaller than that of recently reported circuit analogue absorbers operating in the similar frequency band. Furthermore, a wideband terahertz Hilbert curve array is proposed and analyzed both theoretically and numerically, showing an absorption bandwidth of more than one octave. This was followed by study of plasmonic cloak for subwavelength conducting objects. It was demonstrated that a plasmonic cloak designed for a conducting sphere will work for non spherical conducting objects of similar dimensions as well. Finally spoof plasmonic structures were investigated. A novel plasmonic structure based on a modified Apollonian fractal array of cylindrical coaxial apertures in an aluminium sheet was proposed and analyzed. The structure exhibits negative group velocity with less than 3.5 dB attenuation. Plasmonic structure based on Sierpinski array of apertures was also investigated and found to give quite good extraordinary transmission bandwidth.