In the first part of the talk (based on arXiv:1508.01645) I will present a study of all possible new fermions that can couple to the Higgs, inspecting sets of up to four chiral multiplets. These fermionic extensions of the SM are confront with direct collider searches, electroweak precision tests and our current knowledge of the Higgs couplings. In particular, I will present the regions of parameters where $h\gamma\gamma$ and $hgg$ are unaffected, while the $h\gamma Z$ signal strength is significantly modified. In the second part of the talk (based on arXiv:1512.08508) I will discuss the diphoton excess at 750 GeV, focusing on one particular fermionic extension of the SM with two vector-like quarks. This extension is discussed in the context of a two Higgs doublet model which emerges as a minimal scenario to address at the same time, the diphoton excess and the lepton flavour violating decay into $\tau \mu$ of the 125 GeV Higgs boson.