Mixed precision is an approximate computing technique that can be used to trade-off computation accuracy for performance and/or energy. It can be applied to many error-tolerant applications, but manual precision tuning is both tedious and error-prone. Furthermore, the effectiveness of the technique heavily depends on hardware characteristics. Therefore, a hardware/software co-design approach is necessary for an effective exploitation of precision tuning opportunities offered by the applications. In this paper, we propose, based on the state of the art of precision tuning software and mixed precision hardware, a roadmap for the evolution of hardware designs and compiler-based precision tuning support, which is ongoing in the context of the European projects TEXTAROSSA and APROPOS.