We consider a set of transmitters broadcasting simultaneously on the same frequency under the SINR model. Transmission power may vary from one transmitter to another, and a signal's strength decreases (path loss or path attenuation) by some constant power α of the distance traveled. Roughly, a receiver at a given location can hear a specific transmitter only if the transmitter's signal is stronger than the signal of all other transmitters, combined. An SINR query is to determine whether a receiver at a given location can hear any transmitter, and if yes, which one. An approximate answer to an SINR query is such that one gets a definite yes or definite no, when the ratio between the strongest signal and all other signals combined is well above or well below the reception threshold, while the answer in the intermediate range is allowed to be either yes or no. We describe several compact data structures that support approximate SINR queries in the plane in a dynamic context, i.e., where both queries and updates (insertion or deletion of a transmitter) can be performed e ciently.