We review the recent experimental results from our Nonlinear Physics Center on tunability and nonlinear response
of microstructured metamaterials with negative refractive index. We suggest and design new types of
tunable metamaterials exhibiting either nonlinear magnetic or nonlinear electric response at microwave frequencies.
By introducing a varactor diode as a nonlinear element within each resonator, we shift the frequency of
either magnetic or electric resonance by changing the incident power. We also discuss a novel approach for efficient
tuning of the transmission characteristics of metamaterials through a continuous adjustment of the lattice
structure, the so-called structural tunability. Some of the tuning mechanisms discussed here can be suitable for
scaling toward optical wavelengths with useful applications realizable in a wide frequency range.