Ionically conducting materials (ICMs) are of great importance for the fabrication of portable batteries for electronic devices such as computers, tools, and video and still cameras, and for the development of fuel cell and battery-powered electric vehicles, dye-sensitized solar cells, supercapacitors, and sensors [1].It has been suggested that conductivity in ICMs occurs via a number of different processes. The predominant conductivity processes are attributed to: (a) the migration of ions between coordination sites in the host materials [2][3][4][5], and (b) the increase of conductivity due to relaxation phenomena involving the dynamics of the host materials [2][3][4][5]. Ions "hopping" to new chemical environments can lead to successful charge migration only if ion-occupying domains relax via reorganizational processes [2-5], which generally are coupled with relaxation events associated with the host matrix.In this chapter, the authors concisely describe the instruments used in the comprehensive study of the electric response of ionic conductors. To provide the reader with the basic tools necessary to understand broadband dielectric spectroscopy [6,7], the first part will review the general phenomena and basic theory behind each type of electric response that materials may exhibit when they are subjected to static or dynamic electric fields. This will be achieved by focusing on the practical use of equations, while referring the reader to specialized texts for detailed explanations of the equations. The second part of this chapter