Resumen:

The problem of how the solar corona is hundreds of times hotter than the underlying photosphere continues to be a subject of intense study and interest for the solar physics community. The motivation lies not only on having a detailed account of solar phenomena with potential impact on Earth’s spatial environment, but also on the implicit contribution to understanding the physics of low-density/high-temperature plasmas in other more general astrophysical scenarios. One of the main persisting challenges is that fundamental processes occur on spatial scales that are beyond the resolution power of instruments presently available. Therefore, a strong interaction between models and observations is necessary. From the side of modeling, the highly diverse spatial scales, from single particle gyroradii (cm to tens of m) to the structure of coronal magnetic loops (hundreds of Mm), make it impossible to include all of them in single numerical simulations, demanding instead the use of different approaches and physical formalism for different spatial scale regimes. Regarding observations, it is necessary to put under the same phenomenological frame diverse sets of data obtained in wavelengths spanning from radio to X-rays. In this talk we review the main aspects of the problem, its present state and some of the recent advances in understanding the underlying processes. We discuss also how future missions, instruments and computational tools are expected to contribute to respond key remaining questions.