In this paper, linearly polarized (LP) and circularly polarized (CP) filtering dielectric resonator antennas (DRAs) are presented. They have conducting loops inside them. Equivalent horizontal magnetic dipoles can be obtained from the HEM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{11\delta }$ </tex-math></inline-formula> mode of the DRA and the loop structure. When they are equal in magnitude but opposite in phase, the radiated fields can be canceled out and a good filtering response can be obtained. To demonstrate the idea, both the LP and CP filtering DRAs operating at 2.4 GHz were designed, fabricated, and tested. The reflection coefficient, axial ratio, radiation pattern, antenna gain, and antenna efficiency are studied, and reasonable agreement between the measured and simulated results is found. The LP and CP designs have measured peak realized gains of 5.86 dBi and 5.1 dBic, and out-of-band suppression levels of over 19 and 18 dB, respectively.