From a turbulent history, the study of the abundances of elements in solar energetic particles (SEPs) has grown into an extensive field that probes the solar corona and physical processes of SEP acceleration and transport. Underlying SEPs are the abundances of the solar corona, which differ from photospheric abundances as a function of the first ionization potentials (FIPs) of the elements. The FIP-dependence of SEPs also differs from that of the solar wind; each has a different magnetic environment, where low-FIP ions and high-FIP neutral atoms rise toward the corona. Two major sources generate SEPs: The small "impulsive" SEP events are associated with magnetic reconnection in solar jets that produce 1000-fold enhancements from H to Pb as a function of massto-charge ratio A/Q, and also 1000-fold enhancements in 3 He/ 4 He that are produced by resonant wave-particle interactions. In large "gradual" events, SEPs are accelerated at shock waves that are driven out from the Sun by wide, fast coronal mass ejections (CMEs). A/Q dependence of ion transport allows us to estimate Q and hence the source plasma temperature T. Weaker shock waves favor the reacceleration of suprathermal ions accumulated from earlier impulsive SEP events, along with protons from the ambient plasma. In strong shocks, the ambient plasma dominates. Ions from impulsive sources have T ≈ 3 MK; those from ambient coronal plasma have T = 1 -2 MK. These FIPand A/Q-dependences explore complex new interactions in the corona and in SEP sources.Forbush first observed the effects of SEPs [2], as increases in GeV particles that caused nuclear cascades through the atmosphere to produce what we now call ground-level events (GLEs). These SEPs were visually associated with solar flares and it was commonly assumed that the flares themselves caused SEP events in some way, but there were problems; for example, SEPs that were associated with these flares were eventually found to span more than 180° in solar longitude, which suggests a broad spatial distribution. How could the SEPs from a point-source flare cross magnetic field lines over such a distance? Newkirk and Wenzel [3] proposed the "birdcage" model where SEPs Atoms 2019, 7, 104 2 of 16 could follow coronal magnetic loops that then spread across the Sun like the wires of a birdcage. The birdcage model reigned many years, but Mason, et al. [4] argued that abundances of ions of different rigidity were unaffected by a trip through such a complex magnetic birdcage; they must arise from large-scale shock acceleration. At the same time, Kahler et al. [5] found a 96% correlation between large energetic SEP events and wide, fast coronal mass ejections (CMEs), which had just been discovered several years before. We now know that CMEs drive extensive expanding sun-spanning shock waves, where SEPs are accelerated to produce what we now call "long-duration" or "gradual" SEP events. Considerable controversy arose again with the publication of Gosling's [6] review article entitled "The Solar Flare Myth", which was alleged...