I thought the first place to start the discussion of metallurgy as it applies to bladesmithing is with the definition of the terms that will be used. These words are important. They will allow the exploration of deeper concepts with the correct language to discuss them accurately, in the currently used vocabulary of industry and science.
Annealing: Softening the material so that it can be easily fabricated/machined. There are a number of methods and structures that can be described as annealed. Classic "full anneal" requires that the workpiece be heated to austenitic condition, then cooled very slowly under near equilibrium conditions to produce a structure of coarse pearlite. This is the normal condition for hot rolled bar. Tool steels are usually shipped from the mills in a condition called "spherodize annealed". This consists of a ferrite matrix, with all the carbon as spheroidal carbides of relatively large size scattered evenly throughout the ferrite matrix. This is the most easily machinable condition for hypereutectoid (above .8%C) steels.
Austenite: The solid solution of carbon in iron. In low alloy steels it can normally only exist at elevated temeratures. Face centered cubic crystal, allowing lots of room for carbon atoms. The solubility of carbon is austenite is about 2 %. Addendum 12/11/98. As my good friend Daryl Meier has pointed out to me more than once, austenite by difinition does not require that there be any carbon present. It is what you have when the shift from body centered cubic to face centered cubic structure of the crystal lattice occurs, with or without carbon.
Bainite: The microstructure formed by isothermal transfomation of austenite at temperatures above Ms (martensite start). This is normally used in industry as a heat treatment for springs or other spring-like parts, largely for economic reasons. It does have application in knifemaking, but requires a deeper understanding of the metallurgy to produce, as well as some additional equipment that most may not have. Named after Edgar C. Bain, who nearly re-wrote the entire story of ferrous metallurgy during the 1930's and '40's. His contribution to the understanding of steel cannot be over-emphasized. (in my opinion)
Cementite: Fe3C, iron carbide. Where the carbon goes in steel.
Ferrite: Pure iron, body centered cubic crystal at ordinary temperatures.
Hardening: Heating the workpiece to a temperature above A1 ("critical") to make austenite, then cooling rapidly in some kind of quenchant to produce martensite. (usually martensite is the desired condition, though there are some exceptions like austempering to produce bainite instead)
Martensite: The usual condition that is referred to as "hardened" steel. It is the result of rapid cooling of austenite, trapping the carbon atoms inside the face centered cubic structure, causing them to be greatly distorted into a tetragonal shape that is highly stressed, and thus quite hard. Normally tempered to achieve a comprimise between hardness and "toughness".
Pearlite: The lammelar structure that results from slow cooling from a high temperature. It consists of alternating plates of ferrite and cementite. The spacing of the plates, or relative "fineness" is determined by the temperature at which it was formed, as is the hardness. Fine pearlite can be as hard as HRC 48-50, while coarse pearlite formed by an anneal is usually only HRC 20-25 (numbers given refer to 1075-1095).
Tempering: Re-heating the as quenched martensite to a lower temperature to relieve some of the stress. This lowers the hardness some, but greatly increases the impact resistance, or "toughness". Also precipitates small "temper carbides" out of the martensite as a function of the stress relief.