In this talk, I will present how we can generalize the SIMT execution model of GPUs to general-purpose processors and multi-thread applications, and then use it to design new CPU-GPU hybrid cores. These hybrid cores will form the building blocks of heterogeneous architectures, that will combine CPU-like cores and GPU-like cores which all share the same instruction set and programming model. Beside improving programmability, generalized SIMT enables key improvements that were not possible in the traditional SIMD model, such as simultaneous execution of divergent paths or guarantees of fairness. It opens the way for a whole spectrum of new architectures, hybrids of latency-oriented superscalar processors and throughput-oriented SIMT GPUs.