Soil moisture is an important variable that controls the partition of rainfall into infiltration and run-off. This plays an important role in the prediction of erosion, flood or drought. Passive microwave remote sensing data has great potential for providing estimates of soil moisture. This is mainly due to the minimal weather influence on passive microwave data and its ability to penetrate through clouds. The Artificial Neural Network (ANN) is a method that tries simulates human intelligence by crudely imitating the way a human brain learns. This method has been especially useful for mapping non-linear and ill-posed problems. Soil moisture retrieval is an example of a non-linear problem. An explicit inverse of the physical process can be built using an ANN to map the passive microwave measurements into land surface parameters such as soil moisture. For this paper, the ANN method used to create the explicit inverse function is divided into (i.) single parameter retrieval of the soil moisture value given the passive microwave measurements, and (ii.) multi-parameter retrieval of a number of land surface parameters, i.e. soil temperature, surface roughness, together with soil moisture value given the passive microwave measurements. This paper examines these methods in the context of retrieving surface soil moisture values given microwave radiometric data and discusses key issues that will need to be addressed to improve mapping performance and to produce operational systems.