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Shortly after the seminal paper "Self-Organized Criticality: An explanation of 1/f noise" by Bak et al. (1987), the idea has been applied to solar physics, in "Avalanches and the Distribution of Solar Flares" by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak's own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original papers

-Solar energetic particles (SEPs) constitute an important component of the radiation environment in interplanetary space. Accurate modeling of SEP events is crucial for the mitigation of radiation hazards in spacecraft design. In this study we present two new statistical models of high energy solar proton fluences based on ground level enhancement (GLE) observations during solar cycles 19-24. As the basis of our modeling, we utilize a four parameter double power law function (known as the Band function) fits to integral GLE fluence spectra in rigidity. In the first model, the integral and differential fluences for protons with energies between 10 MeV and 1 GeV are calculated using the fits, and the distributions of the fluences at certain energies are modeled with an exponentially cut-off power law function. In the second model, we use a more advanced methodology: by investigating the distributions and relationships of the spectral fit parameters we find that they can be modeled as two independent and two dependent variables. Therefore, instead of modeling the fluences separately at different energies, we can model the shape of the fluence spectrum. We present examples of modeling results and show that the two methodologies agree well except for a short mission duration (1 year) at low confidence level. We also show that there is a reasonable agreement between our models and three well-known solar proton models (JPL, ESP and SEPEM), despite the differences in both the modeling methodologies and the data used to construct the models.