During the first LHC long shutdown, the CMS collaboration finalised the study of the 8TeV data collected in 2012. Within the impressive amount of results produced, a few searches for new physics show a tension with the prediction from the Standard Model. While the significance is still too small to allow any conclusion, some of these excesses could reveal the first footprint of new processes at the TeV scale. I will discuss a few of these excesses, and give a perspective of the expectation for Run II.