Broad and unexplored kinematic regions can be accessed at the LHC with fixed-target $pp$, $pA$ and $PbA$ collisions at $sqrt{s_{rm{NN}}}=72-115~rm{GeV}$. The LHCb detector is a fully-instrumented forward spectrometer able to run in fixed-target mode, and currently hosts a target gas cell to take data in the upcoming Run 3. The LHCspin project aims at extending this physics program to Run 4 and to bring polarised physics at the LHC. An overview of the physics potential and a description of the LHCspin experimental setup are presented.