The design of nanostructures with increasing complexity and new functionality has garnered significant interest in recent years because of the potential applications ranging from biomedicine, tissue engineering to energy and optoelectronics. Concurrent self-assembly of multiple molecular and/or colloidal amphiphiles has emerged as an important strategy for constructing novel nanomaterials with desired architectures and properties. This review article provides an overview of recent advances in the design, synthesis and assembly behaviors of two or more amphiphiles with competitive or cooperative interactions. We highlight recent contributions on developing strategies of assembling multiple amphiphiles of lipids (or surfactants), block copolymers, and/or inorganic nanoparticles. We briefly outline our perspectives on concurrent assembly, and discuss challenges facing the field from the aspects of theories, experiments, and applications. (C) 2015 Elsevier Ltd. All rights reserved.