The present understanding of cometary ionospheres and plasma tails is critically evaluated. Following a brief introduction of the significance of the study of cometary ionospheres and tails (Section 1), the observational statistics and spectroscopic observations are summarized in Sections 2 and 3. The complicated and time varying morphology of the plasma tail and the ionosphere as revealed both by photographs as well as visual drawings is discussed in Section 4. The evidence for a strong comet-solar wind interaction, the possible nature of this interaction and also the use of comets as probes of the solar wind are considered in the next 3 sections (5, 6, 7). This is followed by a discussion of the various processes so far proposed for the ionization of cometary gases and their limitations (Section 8). Hydrodynamic models of the solar wind-comet interaction, which refers essentially to the region outside the tangential discontinuity, are presented and evaluated in Section 9. A discussion of the ion chemistry and structure of the region inside the tangential discontinuity (which is here referred to as the cometary ionosphere) follows in Section 10. The largely indirect evidence for the existence of substantial magnetic fields in cometary ionospheres and type 1 tails is evaluated and their likely origin is considered in Section 11. The associated electric currents; their size and closure as well as their importance as sources of ionization in the inner coma are also discussed. Finally in Section 12, some of the directions in which future research should progress, in order to provide a more complete and secure knowledge of cometary ionospheres and plasma tails, are stressed.