The energy sector is undergoing several transformations in an effort to tackle climate change, driving society towards reducing energy consumption and more sustainable energy conversion. In this context, electrochemical devices such as Solid Oxide Cell (SOC) technology, play a key role as they can be operated as clean and efficient electricity generator and electrolyzer i.e. converting electrical power into fuel. Both operation modes perfectly suit the energy transition scenario requiring decarbonization of the energy mix, improvement of energy efficiency, and the integration of intermittent renewable energy resources. As an electrolyzer, a SOC system can store the surplus of electricity as chemical energy. As a fuel cell, it can generate electricity and heat with a high efficiency using a wide range of fuels. The challenges that SOC systems have to face in the near term are related to the reduction of costs and to the further extension of their performance and lifetime. A valuable characterization technique to understand the origin of degradations and performance losses during operation is Electrochemical Impedance Spectroscopy (EIS). If specific data analysis is conducted on the recorded spectra, it allows the extraction of information on elementary loss mechanisms and their respective contribution to the overall cell performance. The electrochemical response of a SOC is defined as the sum of the combined mechanisms that are highly convoluted in the frequency domain; thus, their unambiguous identification is only possible with a deconvolution operation. In this thesis, two methods that allow the deconvolution by means of the Distribution of Relaxation Times (DRT) are presented along with their requirements and limitations. Under common operating conditions, a deconvoluted SOC spectrum presents six peaks - i.e. processes - in a frequency range from mHz to hundreds of kHz. The attribution of DRT peaks to a specific process is often obtained by sensitivity analysis of the impedance response under varying operating conditions, e.g. temperature, gas composition, and current density, among others. The position and amplitude of the peaks can change during operation, the attribution of peaks is therefore not univocal and modelling can help to gain further insights. The benefits of using a dynamic numerical model to interpret the observed experimental dependencies of DRT peaks on operating conditions are illustrated in this thesis. The developed model, which includes gas and solid phase transport coupled with charge transfer and chemical reactions in porous electrodes, has been compared to analytical solutions for limiting cases. The knowledge gathered on peaks' attribution, position, and possible evolution was used to analyze long-term experiments. It has been demonstrated that a global performance degradation corresponds to an evolution of the simultaneous improvement and passivation of different phenomena that can only be identified using DRT. Moreover, degradation by sulfur poisoning and its possible performance recovery was analyzed on a different cell architecture, the so-called triode cell. The application of the proposed DRT methodology has proven to be effective for identifying degradation during operation but has limitations as a qualification tool at the end of the production line. This application was demonstrated by applying DRT on impedance spectra recorded from on-purpose faulty stacks.