For environmental reasons, lead has been banned from microelectronic solder materials since the adoption of the RoHS legislation in 2006. A large number of investigations have lead to the development of new lead-free solder materials like the SnAgCu alloy which can satisfy most of the technological requirements. However, the long-time reliability of the lead-free candidates is still a crucial issue and in several cases, failure of electronic assemblies has been attributed to that of the solder joints. To overcome the present challenge in the soldering technology, the damage mechanisms occurring along the service life of lead-free solder joints like microstructure evolution, viscoplastic deformation as well as interfacial cracking must be better understood. The main scope of this thesis is to shed light on the complex interdependency of microstructures, deformation property and the interfacial fracture of solder joints in order to explain the change in the failure mode of solder joints from ductile to brittle interfacial fracture as well as the link between microstructural evolution and the change in the mechanical property of the solders. The first part of this research focused on characterization and macroscopic modeling of the fracture at the interface of SnAgCu solder and Cu substrate with a special attention on the viscoplastic nature of the bulk solder. For this purpose, the viscoplastic behavior of the solder joint was initially identified and the material parameters related to a unified constitutive viscoplastic model were determined. The interfacial fracture behavior of the joint was characterized by performing stable fracture tests at different strain rates. The results confirmed that the failure mode of the solder joint is a function of the loading rate. It was shown that an increase in the loading rate causes a decrease in the load-bearing capacity of the joint by enhancing the tendency to develop an interfacial failure. The interfacial crack propagation in the fracture tests were simulated by developing a detailed three-dimensional (3D) finite element (FE) model containing a cohesive interface and considering the viscoplastic behavior of the bulk solder. The influence of strain rate and viscoplasticity on the load-bearing capacity and failure behavior of the joint were pointed out by analyzing the simulation results. It was shown how the normal stress generated at the interface is limited by the significant viscoplastic relaxation developed in the bulk solder at low strain rates, while a large portion of the external work is transferred to the interface at higher rates which gives rise to interfacial fracture. The second part of this thesis focused on developing microstructure-based models in order to simulate the change in the macroscopic mechanical response of the SnAgCu solder caused by the microstructural evolution during thermal ageing. For this purpose, first, the 3D configurations of microstructures in different ageing conditions were visualized using a combination of synchrotron X-ray and FIB/SEM tomography techniques. Analyses showed that although the size and orientation of crystalline grains as well as morphology of dendrites in SnAgCu solder remain stable during ageing, two main morphological changes occur in the Ag3Sn and Cu6Sn5 intermetallic particles: spheroidizing of needle-shape intermetallics and coarsening due to bulk diffusion. The mechanical property of the solder and its phases at different ageing conditions were experimentally characterized. A significant decrease in the yield strength of the solder joint was identified because of thermal ageing and it was shown that the deformation behavior of the solder is governed by the morphometrics of the dispersed intermetallics. The link between the microstructures and the deformation behavior of solder was successfully simulated by developing a hybrid microstructure-based modeling approach. The average indirect strengthening of the intermetallics was modeled by incorporating the effects of geometrically necessary dislocation on the in-situ deformation behavior of the tin matrix. Subsequently, a micromechanical FE homogenization was considered to model the load-sharing behavior of the intermetallics. For this purpose, the tomographic images were directly used to generate 3D FE meshes of the actual microstructures and then the constitutive deformation behavior of the solder were determined by adopting two levels of numerical homogenization in the eutectic phase and over the whole joint. The decrease in the yield strength of solder due to ageing was explained through analyses of indicators in the models. It was demonstrated how the change in the morphometrics of intermetallics during ageing reduces the contribution of intermetallics in load-sharing as well as the in-situ strength of the matrix by causing a significant change in the strain distribution as well as particle size effects. The simulation results were experimentally verified and the capabilities as well as limitations of the developed approach were pointed out. Overall, the results of this research led to a proper understanding of the critical reliability issues in lead-free solders during isothermal ageing, i.e., microstructural coarsening and interfacial fracture. In addition, through this work, a set of methodologies for multi-scale modeling and experimental characterization of the damage and deformation in solder joints were developed and validated which can be extremely helpful for efficient use of the SnAgCu solders in electronic industry as well as designing new solder alloys with higher strength and better reliability for a safe transition to lead-free solders in critical applications.