The 1980s and 1990s saw seminal works on the role of magnetic helicity in the magnetized solar atmosphere. Thanks to helicity, our understanding of the quiescent and eruptive solar magnetism has progressed substantially since then. From the plausible necessity of coronal mass ejections (CMEs) as sinks of excess solar magnetic helicity in the heliosphere to the solar cycle-independent hemispheric helicity preference, likely imposed by the steady solar differential rotation, to the actual estimates of active-region, quiet Sun, and CME helicities, we have come to place magnetic helicity on equal footing with the electric-current-induced (i.e., non-potential) magnetic energy that fundamentally fuels solar instabilities and eruptions. In spite of this tremendous progress, however, there is still is a lot to learn: first, we need to optimize the way magnetic helicity is practically calculated in local and global solar scales. Then, we need to determine the interplay between different helicity terms that seem to hold distinct aspects of the physics of the system. Furthermore, the role of spectral helicity characteristics, as well as the competition between opposite senses of helicity in a single magnetic structure and its role to eruptions, need to be further clarified. We attempt a resume of what we know, what we are hinted about, and what we should aim to achieve in hopes of spurring a discussion between involved researchers that could further advance the state of the art in the field. This account will be attempted in a plain, physical language to hopefully enable cross-fertilization between different physical domains where helicity is deemed to play a role.

Understanding the physics of solar eruptive activity is a key pursuit of solar physics that continues unabated for at least half a century. Over the past two decades, however, solar eruptions are studied from an additional angle, aiming to generate the necessary operational knowledge to predict them. This has been dictated by recent, vivid interest in space weather forecasting. Moving from understanding to forecasting is a paradigm of research-to-operations (R2O), via which one builds comprehensive databases of quantitative parameters of solar active regions at various stages prior to eruptions. Ranking these parameters in terms of forecasting significance enables another, equally meaningful, step, namely that of operations to research (O2R). In this action, one focuses on the best performing parameters to understand the physics of their (absolute or relative) success. The EU FLARECAST project has managed to collect more than a hundred solar flare (and coronal mass ejection) predictors for each of tens of thousands solar photospheric magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) of the Solar Dynamics Observatory (SDO). With a number of ranking exercises complete, we single out a few of these parameters, whose physics and ramifications for the active-region photosphere and the photosphere-chromosphere coupling we present and discuss. This physics can be boosted from future, ultra high-resolution observations that EST will obtain at high cadence. Therefore, among its other objectives, EST can use existing knowledge to fine-tune its scientific targets, aiming to break ground on the understanding of solar eruptions, potentially even identifying and observing their actual trigger(s). The question of the existence, or lack thereof, of unambiguous eruption precursors is also one of central importance, which EST could successfully put to rest.