Large calculations are done to investigate the valence and inner-valence electronic states of aluminum monochloride and its cationic species AlCl+ and AlCl2+, allowing their definite assignment. This concerns particularly the computations of the potential-energy curves of the electronic states of these species and their spin-orbit couplings and transition moments. An accurate set of spectroscopic constants for these species is also deduced. For the neutral molecule, our calculations show that the lifetimes of the AlCl A(1)Pi v' >= 10 levels are reduced to the 0.1-0.01 ps time scale because of spin-orbit induced predissociation processes and by tunneling through the potential barrier of the A state. Our potential curves for the ground state of AlCl and those of the cationic and dicationic species are also used for predicting the single and double ionization spectrum of AlCl. For both the cation and the dication, long-lived rovibrational levels are predicted.