Assembly injection molding (AIM) provides excellent possibilities for the economical bonding of polymer materials either among themselves or with other materials. Local functionalities can be placed in the product without any restrictions. Typically, different mechanical properties are required, so that the so-called hard-soft material composites that are made from thermoplastics (hard component) and thermoplastic elastomers (soft component) are already established on the market for many decades. Their functionality is focused on damping and sealing properties and comfortable haptic perception as well. Due to the still increasing relevance of these plastic-material composites for new products, it is necessary to further extend the understanding of fundamentals of material bonding mechanisms and knowledge about applications with regard to their adhesive strength and failure behavior. In order to give an up-to-date overview, this work covers therefore the following topics: interfacial effects and compatibility principles, specifics of processing, testing methods for soft-rigid plastic and metal-soft plastic composites as well as test standards, including a discussion of the adhesive strength test results.