Solid-state welding (SSW) is a relatively new technique, and ongoing research is being performed to fulfill new design demands, deal with contemporary material advancements, and overcome welding defects associated with traditional welding techniques. This work provides an in-depth examination of the advancements in the solid-state welding of steels through diffusion bonding (DB) and friction stir welding (FSW). Considerable attention was given to DB of steel, which overcame the difficulties of segregation, cracking, and distortion stresses that are usually formed in liquid-phase welding techniques. The defects that affected DB included two types: two-dimensional defects of a metallic lattice, i.e., phases and grain boundaries, and three-dimensional defects, i.e., precipitation. FSW, on the other hand, was distinguishable by the use of relatively low heat input when compared to fusion welding processes such as tungsten inert gas (TIG), resulting in the formation of a limited heat-affected zone. Moreover, fine grain structures were formed in the FSW interface because of the stirring tool’s severe plastic deformation, which positively affected the strength, ductility, and toughness of the FSW joints. For instance, higher strength and ductility were reported in joints produced by FSW than in those produced by TIG. Nevertheless, the HAZ width of the specimens welded by FSW was approximately half the value of the HAZ width of the specimens welded by TIG. Some defects associated with FSW related to the diffusion of elements, such as C/Cr atoms, through the weld zone, which affected the local chemical composition due to the formation of rich/depleted regions of the diffused atoms. Moreover, the lack-of-fill defect may exist when inappropriate welding conditions are implemented. On the other hand, the stirring tool was subjected to extensive wear because of the high hardness values, which negatively affected the economical usage of the FSW process. A summary of the results is presented, along with recommendations for future studies aimed at addressing existing difficulties and advancing the solid-state technology for steel.