When the carrier frequency of a laser pulse fits to the energy difference between two electronic states of a molecule, the potential energy surfaces of these states dressed by the field become energetically close and the states can couple strongly to each other. Recently, it has been predicted that for diatomic molecules these surfaces may exhibit a conical intersection induced by the laser light in the space of the nuclear internal and external coordinates. Here, we report a general theory of the light-induced conical intersections emerging in polyatomic molecules where additional internal degrees of freedom are involved in the dynamics. Freely rotating and also fixed-in-space arbitrary polyatomic molecules exposed to differently polarized optical laser pulses of resonant carrier frequency are considered. Detailed analysis of the theory shows how the light-induced conical intersections can be controlled by molecular orientation and by the carrier frequency, polarization, strength, and duration of the laser pulse. This opens the possibility to also control the ensuing non-adiabatic dynamics. Different strategies of exploitation of the light-induced conical intersections are proposed. The present theory is exemplified by utilizing the light-induced conical intersections to control photodissociation of the second electronically excited state S2 of the fixed-in-space cis-methyl nitrite CH3ONO.