On the Sun, the presence of magnetic flux at the photosphere is closely linked to (1) steady heating of the overlying atmosphere and (2) transient brightenings, the largest of which are flares.   I will discuss statistical properties of both phenomena, with an emphasis on aspects of each that might apply to other astrophysical objects, such as other stars or stellar remnants, and perhaps AGNs.  Regarding heating, power-law scalings have been found to relate magnetic flux with steady coronal emission in both soft X-ray (SXR) and EUV ranges.  A key observation is that the details of magnetic structure (field strengths and their spatial gradients, including measured electric currents) appear not to affect heating rates. Similar SXR scalings have been reported for G,K, and M dwarfs and classical T-Tauri stars.  Departures from such scalings, whether on the Sun, other stars, or other objects, might reveal important aspects of the heating mechanisms that drive steady emission, and should be sought.   Regarding flaring, again a power-law scaling between magnetic flux and flare SXR emission has been found, but with a different exponent.  Differences in these scalings suggest that steady heating fundamentally differs from flare heating, disfavoring the “nanoflare” hypothesis (i.e., that steady coronal heating arises from many weak, unresolved flares that are essentially scaled-down versions of larger flares).  Analogous differences in the scalings of steady vs. flaring luminosities with magnetic flux on other objects could constrain processes driving each type of emission.  Another key property of flares is that they extract energy from the magnetic field, which in the solar case leads to measurable changes in field strengths after flares – photospheric field strengths tend to increase, coronal fields tend to decrease.  It is possible that analogous changes could be observed on other stars or objects (via, e.g., Zeeman or synchrotron  methods).