Recent advances and open challenges in percolation
  Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation. 
N. A. M. Ara\'ujo, P. Grassberger, B. Kahng, K. J. Schrenk, R. M. Ziff
cond-mat.stat-mech