"YAKI-IRE" The Japanese term for the practice of hardening a blade. This is NOT tempering the blade. Tempering actually means to soften a blade after the cutting edge has been hardened. The smith does the tempering to prevent the rest of the knife/sword from being too brittle. In Japanese swords, shingane is used to create a softer center of the sword. It causes the steel to be flexible, yet with a sharp edge. In European swords, the same metal is used in the whole sword, but the back of the blade (usually the whole length of the shinogiji) is heated again, and becomes soft. Thereby the sword is still flexible, but stays sharp at the edge.
When hardening the steel a master can make several distinct areas of steel structure within the blade. The hamon line is a border between the hardest structure (martensite) and the milder structure at the back of the blade. There are various sizes of discrete martensite crystals. The smallest particles are called Nioi these are not visible as particles by eye, Then there are larger particles called Nie that are visible within the blade. When a sword is polished properly these look a bit like white dots and the hamon line will look like a white line. There are also white lines that are made up during the modern style of polishing. These are fake hamons. To see a real hamon in modern polishing requires a good light and letting the light reflect on the cutting surface of the blade. Relax your arms and keep the blade at a distance from your eyes. When you get the right angle between the blade surface and the light, the real hamon becomes very visible and practically jumps out at you as a white line. This way of looking at a blade will also show a fake hamon as just that fake, AND if you are lucky enough to have one you can also see shadow hamon, known as Utsuri.
Hamon patterns are classified in two groups, Suguha, which is a straight hamon and Midareba the irregular hamon. Then these two kinds are classified again into many sub types.
Keep in mind that an aesthetic hamon pattern doesn't mean it is a good hamon. The "pattern" is just a matter of personal preference, when evaluating a hamon the brightness and the fineness of the particles of the hamon, not only in the hamon line but also the entire hamon area, is a bigger criterion of the quality.
Traditional hamons are "sort of" designed by the smith and how he clays the blade and uses the water and fire. So specific hamon are unique to a school because they teach the way they make that hamon. BUT traditional Smiths do not design the hamon pattern with clay. The area near the cutting edge is uncoated with clay at all. The traditional Smith just uses the clay to suppress hardening in an area on the spine. The detail of the hamon is designed by Nature, based on the steel, the fire and the use of the water. Now modern Smiths can design hamon patterns with clay, putting ashi or yo to design a very specific hamon shape. Modern master smiths can make the hamon exactly as they want it to look, and it is just as much a hamon as any traditional one. However, the WAY the hamon is created is different in the way the clay is used to pattern. Not just protect.
Utsuri is actually the 2nd "level" hardened steel. It is softer than the edge, yet tougher than the back. Prior to the 17th century almost every Nihonto has Utsuri since then it is sometimes there sometimes not. It does however show extremely well hardened steel in the Japanese swordmaking world. Again the shape is less important than the quality of the particles and the color of the shadow. However, as with Hamons, someone who KNOWS Nihonto can tell Era and school from the shape and size of the Hamon or Utsuri. The process of creating them were handed down by masters of each school to their apprentices. In some cases though a specific Hamon can tell an expert exactly which Master Smith made a blade.