Since nowadays most complex software systems are intrinsically multi-paradigm, their engineering is a challenging issue. Multi-Paradigm Modeling (MPM) aims at facing the challenge by providing concepts and tools promoting the integration of models, abstractions, technologies, and methods originating from diverse computational paradigms. In this paper we survey the main MPM approaches in the literature, evaluate their strengths and weaknesses, and compare them according to three main criteria—namely, i) the software development process, ii) the adoption of meta-model techniques, iii) the availability of adequate supporting tools. Furthermore, we explore the adoption of other promising approaches for the engineering of multi-paradigm systems, such as Multi-Agent Systems (MAS) and Systems of Systems (SoS), and discuss the role of Situational Process Engineering (SPE) in the composition of multi-paradigm software processes.