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One of the hallmarks of engineering design is the design synthesis phase where the creativity of the designer most prominently comes into play as solutions are generated to meet underlying needs. Over the past decades, methodologies for generating concepts and design solutions have matured to the point that computation-based synthesis provides a means to explore a wider variety of solutions and take over more tedious design tasks. This paper reviews advances in function-based, grammar-based, and analogy-based synthesis approaches and their contributions to computational design synthesis research in the last decade.