The temperature rise at the interface of two sliding bodies has significant bearing on the friction and wear characteristics of the bodies. The friction heat generated at the interface can be viewed as "loss of exergy" of the system, which also leads to accelerated wear in the form of oxidation, corrosion, and scuffing. This has a direct impact on the performance of the components or the machinery. If the sliding interface is also conducting electric current then the physics at the interface becomes complicated. The presence of electrical current leads to Joule heat generation at the interface along with other effects like electromotive, electroplasticity, stress relaxation and creep. The interface of an electrical contact, either stationary or dynamic, is a complex environment as several different physical phenomena can occur simultaneously at different scales of observations. The main motivation for this work stems from the need to provide means for accurate determination or prediction of the critical contact parameters viz., temperature and contact resistance. Understanding the behavior of electrical contacts both static and dynamic under various operating conditions can provide new insights into the behavior of the interface. This dissertation covers three major topics: (1) temperature rise at the interface of sliding bodies, (2) study on static electrical contacts, and (3) study of factors influencing behavior of sliding electrical contacts under high current densities. A model for determining the steady-state temperature distribution at the interface of two sliding bodies, with arbitrary initial temperatures and subjected to Coulomb and/or Joule heating, is developed. The model applies the technique of least squares regression to apply the condition of temperature continuity at every point in the domain. The results of the analysis are presented as a function of non-dimensional parameters of Peclet number, thermal conductivity ratio and ellipticity ratio. This model is first of its kind and enables the prediction of full temperature field. The analysis can be applied to a macro-scale contact, ignoring surface roughness, between two bodies and also to contact between two asperities. This analysis also yields an analytical expression for determining the heat partition between two bodies, if the Jaeger's hypothesis of equating average temperatures of both the bodies is being implemented. In general for design purposes one is interested in either the maximum or the average temperature rise at the interface of two sliding bodies. Jaeger had presented simple equations, based on matching the average temperatures of both bodies, for square and band shaped contact geometries. Engineers since then have been using those equations for determining the interface temperature for circular and elliptical shaped contact geometries. Curve fit equations for determining the maximum and the average interface temperature for circular and elliptical contact with semi-ellipsoidal form of heat distribution are presented. These curve fit equations are also applicable for the case when both the bodies have dissimilar initial bulk temperatures. The equations are presented in terms of non-dimensional parameters and hence can easily be applied to any practical scenario. The knowledge of electrical contact resistance between two bodies is important in ascertaining the Joule heat generation at the interface. The prediction of the contact resistance thus becomes important in predicting the performance of the contact or the machinery where the contact exists. The existing models for predicting ECR suffer from the drawback of ambiguity of the definition of input parameters as they depend on the sampling resolution of the measuring device. A multi-scale ECR model which decomposes the surface into its component frequencies, thus capturing the multi scale nature of rough surfaces, is developed to predict the electrical contact resistance. This model, based on the JS multi-scale contact model, overcomes the sensitivity to sampling resolution inherent in many asperity based models in the literature. The multi-scale ECR model also offers orders of magnitude of savings in computation time when compared to deterministic contact models. The model predictions are compared with the experimental observations over a wide range of loads and surface roughness of the specimens, and it is observed that the model predictions are within 50% of the experimental observations. The effect of current cycling through static electrical contact is presented. It is observed that, the voltage drop across the contact initially increases with current until a certain critical voltage is increased. Beyond this critical point any increase in the current causes essentially no increase in steady-state contact voltage. This critical voltage is referred to as "saturation voltage." The saturation voltage for Al 6061 interface is found to be in the range of 160 - 190 mV and that for Cu 110 interface is in the range of 100 - 130 mV. The effect of load and surface roughness on voltage saturation is also demonstrated experimentally. An explanation based on the softening of the interface, due to temperature rise, is proposed rather than more widely referred hypothesis of recrystallization. The phenomenon of voltage saturation is also demonstrated in sliding electrical contacts. The behavior of sliding interfaces of aluminum-copper (Al-Cu) and aluminum-aluminum (Al-Al) are analyzed under high current densities. Experimental results are presented that demonstrate the influence of load, speed, current and surface roughness on coefficient of friction, contact voltage, contact resistance, interface temperature and wear rate. The experimental results reveal that thermal softening of the interface is the primary reason for accelerated wear under the test conditions. The results from the experiments presents an opportunity to form constitutive equations which could be used to predict the performance of the contact based on input parameters. The fusion of the findings of this dissertation provide methodologies along with experimental tools and findings to model, study and interpret the behavior of electrical contacts.