For the past five decades, hundreds of unfinished public works have been erected in Italy as the result of inconsistent planning and the presence of corruption and organised crime. A third of these constructions are located in Sicily alone and so, in 2007, a group of artists labelled this phenomenon an architectural style: 'Incompiuto Siciliano'. Through this creative approach, the artists' objective is to put incompletion back on the agenda by viewing it from a heritage perspective. This article reviews the different approaches that the artists have envisaged to handle unfinished public works; whether to finish them, demolish them, leave them as they are or opt for an 'active' arrested decay. The critical implications of these strategies are analysed in order to, ultimately, conclude that incompletion is such a vast and complex issue that it will surely have more than one single solution; but rather a combination of these four. This is important because it opens up a debate on the broad spectrum of possibilities to tackle incompletion-establishing this as one of the key contemporary urban themes not only in Italy but also in those countries affected by unfinished geographies after the 2008 financial crisis.