Perimeter and ring currents induced in planar monocycles and polycycles by perpendicular magnetic fields are commonly taken as diagnostic of aromaticity and antiaromaticity in these systems. Diatropic pi currents are associated with aromaticity, paratropic with its opposite. The ipsocentric method is an accurate and economical way of calculating ab initio current-density maps. In pi systems it provides a natural interpretation of ring currents in terms of nonredundant orbital contributions, governed by simple symmetry rules for pi-pi* virtual excitations and dominated by the frontier electrons. Thus, in planar [4n + 2] monocycles, the product of pi HOMO and pi* LUMO symmetries includes that of the in-plane translations and leads to a 4-electron diatropic current. In planar [4n] monocycles, this product includes the symmetry of the in-plane rotation and leads to a 2-electron paratropic current. Perturbation arguments based on the monocycle explain the opposite senses of the pi ring currents in naphthalene (diatropic) and pentalene (paratropic) as consequences of their different frontier-orbital symmetry products. In a generalization to heterocycles, ring current maps for benzotriazole (BtH), its conjugate base (Bt(-)) and the cation (Bt(+)) are calculated at an ab initio level. The diatropic current of the two 10pi systems and the paratropic current of the 8pi system are rationalized in terms of the perturbed-annulene orbital model, giving an explanation of the applicability of simple electron counting in these cases: where the frontier-orbital structure remains close to that of the [4n+2]/[4n] annulene, so does the current-density map.