Heavy-ion physics at the LHC: Review of Run I results

In this work we review what we consider are, some of the most relevant results of heavy-ion physics at the LHC. This paper is not intended to cover all the many important results of the experiments, instead we present a brief overview of the current status on the characterization of the hot and dense QCD medium produced in the heavy-ion collisions. Recent exciting results which are still under debate are discussed too, leading to intriguing questions like whether we have a real or fake QGP formation in small systems.