Abstract: Both stationary and time dependent adjoint problems associated to advection-diffusion problems are formulated. The adjoint problem is then interpreted as a model for an advection-diffusion process of a tracer called the "adjoint tracer". The construction of such a model is a sine qua non condition for the integration of the adjoint advection-diffusion equation by means of probabilistic methods. A reciprocity relation relating direct and adjoint transition probability density functions is derived. Strategies to solving advection-diffusion problems by means of Monte Carlo methods are illustrated.