The interplay between the exponential improvement of experimental techniques at the nanoscale and theoretical development in quantum technologies has led the community to consider how to extend the well-established laws of thermodynamics to small quantum systems which cannot be described by the so-called thermodynamic limit. This has led to the blossoming of quantum thermodynamics which is extending concepts of heat, work, and entropy to few-particle quantum systems. Quantum thermodynamic formalism must also include additional quantities such as quantum coherence and entanglement which may affect behaviours of small quantum systems and can lead for example to novel concepts or resources for thermodynamics machines. In addition, actual quantum technology devices necessitate finite temperatures description and usually their protocols correspond to non-adiabatic out-of-equilibrium regimes. Understanding of these devices implies the development related finite-time, out-of-equilibrium quantum thermodynamic formalism. In small quantum systems, many-body interactions may have particularly dramatic effects: they may drive or destroy desirable entanglement and quantum coherence within the system; they may be responsible for precursors to Mott-insulator quantum phase transitions; they may lead to the destruction of quantum coherence through entanglement of the quantum system with the environment; their strength may determine the level of memory in the interaction between the system and its bath; they may also affect the dynamical regime of a system, for example with respect to how close it is to adiabaticity. Many questions remain open with respect to the effects of many-body interactions, on quantum thermodynamics, and a better understanding would be welcome on issues such as: the role of many-body interactions for quantum particles driven out of equilibrium, and how do they affect quantum thermodynamical quantities; do they contribute or oppose reversibility and thermalization; are there signatures of many-body interactions in thermodynamic distributions, for example across quantum phase transitions; do these effects depend on the system size; can we engineer many-body interactions to improve quantum machine efficiency; how can we probe a many-body quantum fluid to measure the work obtained from a thermodynamic protocol; etc. In this mini-colloquium we will review recent advances in quantum thermodynamics with a particular emphasis on the effects of many-body interactions.