The Sun represents a template for much of our understanding of the workings of a "cool" star, and its proximity allows us to observe exquisite details at its surface, with current facilities routinely reaching resolutions of few hundreds of km on the solar disk. Yet, many questions still linger, in particular concerning the actual mechanism(s) that create and maintain a hot outer atmosphere (chromosphere, transition region and corona) as well as the solar wind. We know that a major role is played by the magnetic field, that mediates the transfer to the upper atmosphere of the abundant energy provided by surface convection. However, very little is currently known about the field itself in these upper layers, owing to the difficult of measuring and interpreting the weak polarization signal created by its presence. Similarly, in the outer atmosphere we observe a dazzling variety of small and highly dynamic features that are often invoked as responsible for providing mass and energy to the corona; yet big uncertainties exist on their physical characteristics due to the small scales involved. In this talk I will focus on some of these open questions, and discuss how progress from upcoming observational facilities will improve our understanding of the magnetic and thermodynamic structure of the solar atmosphere. In particular, I will describe the possibilities provided by the Daniel K. Inouye Solar Telescope (DKIST) of the US National Science Foundation, a 4-meter facility on the island of Maui, Hawai'i, which is currently being commissioned. With its unprecedented collecting area and suite of complementary instruments, DKIST will provide the highest-resolution observations of the Sun ever achieved, as well as the sensitivity to measure the vector magnetic field in the chromosphere and in the faint corona.