The proliferation of sensing device technologies, and the growing demand for data intensive IoT applications, are paving the way to the next wave of transformation in IoT computing systems architecture. The goal today is to design, implement and deploy a seamless interconnection of IoT, edge and cloud resources in one computing system, to form a compute continuum, also referred to as edge-to-cloud. In this talk, compute continuum refers to the deployment and execution of self-adaptive machine learning-based applications employing IoT sensors. Because of their distributed nature over constrained resources devices, these applications leverage the cloud infrastructure for learning tasks while exploiting edge devices for inference tasks on data coming from local IoT sensors. But the next wave of development is already underway; it will involve designing edge-to-edge platforms where learning takes place locally. A coordination platform is used to exchange intelligence between the edges. This talk will be organised as follow: (1) why and what is continuum computing? (2) A comparative study of continuum computing solutions, (3) a cloud continuum platform deployed on edge-to-edge infrastructure and supporting distributed federated learning (FL) applications and (4) an example of a FL based IoT application, for smart grid and renewable energies, deployed on an open source distributed continuum computing solution. This talk is the result of two European projects: SWARM and LASAGNE.