Tidally synchronized planets present a new opportunity for enriching our understanding of atmospheric dynamics on planets. Subject to an unusual forcing arrangement (steady irradiation on the same side of the planet throughout its orbit), the dynamics on these planets may be unlike that on any of the Solar System planets. Characterizing the flow pattern and temperature distribution on the extrasolar planets is necessary for reliable interpretation of data currently being collected, as well as for guiding future observations. In this paper, several fundamental concepts from atmospheric dynamics, likely to be central for characterization, are discussed. Theoretical issues that need to be addressed in the near future are also highlighted.