Well, first, let's go into some history.
A habitable zone around a main sequence star was originally (1959) defined as a (virtual) ring around that star in which at least 10% of the surface of a planet, with an Earth-like atmosphere, in that zone had a mean temperature of between 0 and 30 C with extremes not exceeding -10 and 40 C. This is appropriate for humans to survive.
The zone was quickly expanded to mean wherever liquid water was stable. The term "biostable" was employed to mean where liquid water was stable and the term "habitable" was restricted to mean a place suitable for humans. Soon, though, "habitable" was expanded to replace "biostable" and to include anywhere that liquid water is stable.
All (peer-reviewed) models since the original definition have used one type of atmosphere or another, usually an atmosphere chemically similar to Earth's. Most have also considered planetary albedo (surface brightness), solar evolution (as a star moves along the main sequence, the habitable zone changes or disappears, depending on the details), etc.
Several models have pessimistic estimates to the width and/or lifetime of a habitable zone, most often because an atmosphere like the Earth's is only metastable and it could collapse with only a few % change in solar energy input (distance from or luminosity of the sun, for example can greatly affect the stability of an atmosphere). Other models have included climate stabilization by linking CO2 and surface processes such as the creation/weathering of certain types of rock that remove/add CO2 from/to the atmosphere. There are a lot of these kinds of details that are included in most models of the habitable zone. A lot of the work is in determining which details are more important than others.
For my graduate work, we had to define the habitable zone around the sun, at the beginning of the solar system (4.556 Ga), and now. To do so, we had to start from the proplyd, condense all of the elements at the right distances from the sun, build the planets (we were allowed to assume that they formed in their current positions unless we wanted to make our work more difficult), allow atmospheres to condense or form, depending on where the planets were, etc., and finally determine which planets were possibly in the habitable zone as the sun evolved (Venus, Earth, and Mars, depending on the details and assumptions), and then determine whether the planets that are here now are in the habitable zone, and why or why not.
We, of course, used some pretty simple 1-D models for atmosphere, or used published models and argued why they were valid. We used simple models for planetary albedo, didn't evolve the albedo unless the atmosphere collapsed or changed dramatically in some other way (ignored Earth-like clouds, for example), etc. We used simple estimates for the concentrations of radioactive elements that could contribute to the surface temperature, used a simple model for luminosity evolution, etc., etc., etc.
For these kinds of simple models, the inner edge of the habitable zone is defined by when water will be lost from the atmosphere (through photolysis of the water vapor and escape of the hydrogen) and the outer edge is defined by when CO2 condenses and causes runaway glaciation.
Technically, the Moon is within the habitable zone, but it's obviously not habitable. Neither are Venus or Mars. This is because they don't have the right atmosphere, and may never have had the right conditions.