The quantum internet is envisaged to connect quantum systems at a global scale to provide diverse applications unimaginable with the classical internet. However, the technological shortcomings and practical challenges of noisy intermediate-scale quantum (NISQ) devices impose several constraints on the vision of a truly global quantum internet. Recent experimental developments for quantum networks are laying the pathway from small-scale to intermediate-scale noisy quantum networks dedicated to specific operational tasks. Although these networks are not at the global scale, they are capable of providing a clear quantum advantage in their dedicated tasks. We explore the cardinal features of these NISQ networks, discuss their design constraints, and explore the possible applications they provide. We also outline some technical challenges that need to be addressed for the practical implementation of these networks and eventually lead toward a truly global, fully functional quantum internet.