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The planarization method is the strongest known method to heuristically find good solutions to the general crossing number problem in graphs: Starting from a planar subgraph, one iteratively inserts edges, representing crossings via dummy vertices. In the recent years, several improvements both from the practical and the theoretical point of view have been made. We review these advances and conduct an extensive study of the algorithms' practical implications. Thereby, we also present the firstdoi:10.7155/jgaa.00264 fatcat:c6z5aesvkbdxhhmg6ketj7ukia