Active metamaterials are a group of artificial electromagnetic structures that employ active electronic circuits. They are characterized by specific properties, such as amplification, non-reciprocal response, dynamic reconfigurability and dynamic tunability, in addition to properties associated with passive metamaterials. Instability is the most challenging problem facing active metamaterials, especially those incorporating negative elements. The thesis includes a detailed stability analysis of lumped and distributed networks commonly used in modeling of active non-Foster metamaterials. The proposed stability analysis is applied to the model of metasurface-based PT-symmetric system. Finally, the analysis, synthesis, fabrication and experimental verification of passive and active reflective polarization converting metasurfaces are presented. The detailed stability analysis reveals that closed-form stability criterion can be derived only for specific types of distributed networks with negative elements. Some distributed networks are proven to be inherently unstable. Dispersion of a negative element is proposed as a solution to the stability problem. Furthermore, a closed-form stability criterion is derived for the model of PT-symmetric system. The analysis shows that every PT-symmetric system is necessarily marginally stable. Finally, stable operation of the active metasurface was ensured and verified. The desired effects of amplification, polarization conversion, polarization selectivity and non-reciprocal response were successfully demonstrated.