The present state of both our knowledge and our understanding of cometary atmospheres and their interactions with the solar wind is critically reviewed. Following the introduction (section 1) the spectrophotometry of the cometary atmosphere and the tail is reviewed in section 2. The existing, rather fragmentary, knowledge about atmospheric abundances and the production rates of various molecular species is given in section 3. The deductions that can be made from these values about the chemical composition of the nucleus and their uncertainties are discussed. Existing models of the cometary atmosphere including the ionosphere are critically evaluated in section 4. The continuing dichotomy between models that concentrate on the chemistry while oversimplifying the dynamics and those that concentrate on the dynamics and thermodynamics while minimizing the chemistry is discussed. The need to combine these two approaches in the future is emphasized. The ionization processes in the cometary atmosphere are discussed in section 5. It is emphasized that besides photoionization and charge exchange ionization with the solar wind protons, other (collisional) ionization processes may play a role in the rapid ionization of cometary neutrals in certain situations. The overall nature of the solar wind‐comet interaction is discussed in section 6 with special emphasis on the strong coupling between the solar wind and cometary plasmas, which is responsible for the observed accelerations in the cometary tails. The complex and time‐varying fine structures observed in the plasma tails of comets are discussed next in section 7. The uses of these to infer the strength and morphology of the magnetic field and the associated currents in the plasma tail on one hand, and the varying conditions in the solar wind on the other, are emphasized. The detailed models of the comet‐solar wind interaction, from the earlier fluid dynamic models to the latest MHD models are critically evaluated in section 8, and their limitations are underscored. It is also pointed out that the nature of the solar wind interaction with the cometary atmosphere is highly variable and that in certain circumstances the nature of both the outer and the inner shocks could change. Also, the need for a detailed study of the solar wind interaction with the fledgling cometary atmosphere at larger heliocentric distances is stressed. The review is concluded with section 9, where the emphasis is on the outstanding problems of cometary atmospheres and their interactions with the solar wind.