Solder joints play a critical role in electronic devices by providing electrical, mechanical and thermal interconnections. These miniature joints are also the weakest links in an electronic device. Under severe thermal and mechanical loadings, solder joints could fail in 'tensile fracture' due to stress overloading, 'fatigue failure' because of the application of cyclical stress and 'creep failure' due to a permanent long-term load. This paper reviews the literature on solder joint failures under thermo-mechanical loading conditions, with a particular emphasis on fatigue and creep failures. Literature reviews mainly focused on commonly used lead-free Sn-Ag-Cu (SAC) solders. Based on literature in experimental and simulation studies on solder joints, it was found that fatigue failures are widely induced by accelerated thermal cycling (ATC). During ATC, the mismatch in coefficients of thermal expansion (CTE) between different elements of electronics assembly contributes significantly to induce thermal stresses on solder joints. The fatigue life of solder joints is predicted based on phenomenological fatigue models that utilise materials properties as inputs. A comparative study of 14 different fatigue life prediction models is presented with their relative advantages, scope and limitations. Creep failures in solder joints, on the other hand, are commonly induced through isothermal ageing. A critical review of various creep models is presented. Many of these strain ratebased creep models are routed to very well-known Anand Model of inelastic strain rate. Finally, the paper outlined the combined effect of creep and fatigue on solder joint failure.