Intelligent systems have emerged in our biosphere in different contexts and achieving different levels of complexity. The requirement of communication in a social context has been in all cases a determinant. The human brain, probably co-evolving with language, is an exceedingly successful example. Similarly, social insects complex collective decisions emerge from information exchanges between many agents. The difference is that such processing is obtained out of a limited individual cognitive power. Computational models and embodied versions using non-living systems, particularly involving robot swarms, have been used to explore the potentiality of collective intelligence. Here we suggest a novel approach to the problem grounded in the genetic engineering of unicellular systems, which can be modified in order to interact, store memories or adapt to external stimuli in collective ways. What we label as Synthetic Swarm Intelligence defines a parallel approach to the evolution of computation and swarm intelligence and allows to explore potential embodied scenarios for decision making at the microscale. Here, we consider several relevant examples of collective intelligence and their synthetic organism counterparts.