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Discrete object modelling has been used since the beginning of airborne electromagnetic exploration. A recent effort of integrating existing modelling and inversion tools with airborne data shows that simple models are still quite useful for exploration. They can provide simple parameters of a model with minimum a priori and still provide adequate data fitting. Approximations allow using models with reasonable computer resources. Plate models have been popular and inversion programs have been developed around them. Another inversion approach is based on approximation of sphere or plate response in free-space. Finally, a recent development is an analytic solution for a conductive sphere in a layered earth. We present some applications of this methodology.