In this book, we provide a general vision of four main aspects of the low-temperature liquid phase of helium-4, often named He II or Helium II or superfluid helium, and quantum turbulence from the perspective of non-equilibrium thermodynamics. The first one is a comparison of the standard two-fluid model and a one-fluid extended model of Helium II and their respective merits in providing complementary descriptions of this fascinating physical system. The second aspect is a thorough analysis of the rich phenomenology of heat transport in superfluid helium, including an analysis of quantum turbulence, its generation, its physical features, and its consequences on heat transport. The third aspect is devoted to a comparison of quantum and classical turbulence, from the points of view of the closure of the hierarchy of moments of fluctuations and of the main features of energy cascades in turbulence. The fourth aspect is a discussion of some analogies between the thermodynamics of turbulent vortex tangles and the thermodynamics of cosmic strings, its cosmological consequences and some dualities between the thermodynamics of photons and of cosmic string loops. Emphasis is provided on non-equilibrium thermodynamic methods, superfluid heat transport phenomenology, macroscopic dynamics of quantum turbulence, and formal explorations on temperature and entropy beyond local equilibrium states.