The applications of CV and EIS typically involve any process where electrochemical (typical RedOx) processes take place. These may range from corrosion to electroplating/coating to dye/pollutant sensing, to Energy storage (Batteries and supercapacitors)
the CV and EIS application depend on the materials you are interested. I'm working on batteries so I use CV to determine the redox couples of the elements active in the analysed electrochemical window, the diffusion coefficient, the pseudocapacitive or diffusion mechanism of the intercalation process. EIS data provide for example the values of the different types of resistances acting in an electrochemical cell.
In order to characterize electrochemical electrodes and cells electrically one needs to measure their I-V characteristics upon scanning the applied voltage in forward and reverse direction in acyclic manner. By analyzing these curves one can information about the charge transfer processes at the electrolyte electrode interface.
The EIS the electrochemical impedance spectroscopy where one one biases the device electrode at certain DC bias and then measure the complex impedance of the electrode. One gets from these complex impedance plots the conductive and the capacitive components of the current transfer across the interface and speed of such transfer.
There is also similar characterization to the semicondcutor devices such as the p-n junctions.
For such analogy please see the presentation in the link:Presentation The properties of electrodes and electrochemical cells for w...