http://en.wikipedia.org/wiki/Japanese_swordsmithing
A couple of the claims written in the answers above need to be discussed with counter points;
The ancient Japanese samurai sword that we are talking about was specifically developed to address the brittle nature of steel that time, no it was not brittle by yesterday's standard or today's.
Precisely because of the brittle issue in steel, the katana was developed using a technique consisting of three types of metal, the center was soft, that was sandwiched by harder folded steel
The folding does more then simply homogenize the carbon content or knock out the carbon, in fact carbon was added between layers as the smith thought needed, they had an experienced feel for too much or too little carbon during their forging process
Folding does more then remove impurities, the folds seem to add a level of strength and pliability, or "toughness", a grain is produced that could also be manipulated to add differentiating strengths to different areas in the blade, like alternating the grain of hardwood. I am not sure when differentiating the grain is added to the process, or how many and which smiths actually did it.
After that folding and sandwiching process, the folding then is not the same as done today, there were layers of other products added between folds with indigenous ingredians, this "recipe" is probably lost, though some smiths in japan claim to still have it carried down.
The edge was case hardened further in a process known as "clay tempering", different types of clay insulating the blade to different degrees to produce different levels of hardness in the final forging process.
The edge of the blade had to be hard to maintain that sharpness, combining the different types of metal in the body and edge is now called "lamination", there were different methods for combining and welding the three types of metal, I some far more elaborate then others, an authentic katana is NOT simply folded steel, it's folded AND laminated, AND clay tempered.
That painstaking procedure was specifically designed so the entire sword would not be brittle as claimed in above answers, the lore reports, in the first battle using this "new method" of lamination, not one sword returned broken, it was not only the folded steel that produced the superior toughness, the "recipe, the nano tubes, the lamination. Most reproductions today do not use a multi steel lamination, though "some" of the more expensive reproductions might.
Additionally, metallurgists have performed forensics and discovered the original katana did indeed enjoy "nanotubes, nanowires" and "impurities" like tungsten and vanadium, "impurities" that made the steel both hard and flexible, stronger then one might get using unfolded unlamenated modern carbon steel. (I believe swedish powdered steel has tungsten and vanadium added in their forging process.)
http://en.wikipedia.org/wiki/Bladesmith
"One is the true Damascus steel, or Wootz steel, which is a high carbon alloy with tremendous edge retention possibly due to its composition of carbon nanotubes and carbide nanowires,[17] with a wavy surface texture originating from the crystalline structure of alloy metals such as tungsten and vanadium - elements that occur naturally in iron ore from southern India - to the surface during the manufacturing process"
The curve in the katana isn't cut or bent by the swordsmith, it was a happy consequence of the "new" forging process, the bend that occurs when the different steels are cooled in the clay tempering process, though the experienced smith could and would influence the nature of the curve.
I have no idea how an authentic ancient katana would compare to a sword made from Swedish powdered steel, I don't think anyone who possesses an ancient Katana would be willing to donate it for destruction comparison.
However tests have been conducted comparing the long sword of the era vs the katana, in the test I am posting, the katana is a "modern" made katana that does NOT use lamination.
Nor does the metal in this youtube have the nano tubes and nano wires that added more toughness and durability to the steel, in other words, it's not likely the samurai sword in the demo is as good a weapon as the ancient katana, but the same could be true about the broadsword
The katana wins every test in this modern comparison, it wins as a slashing weapon, as a penetrating weapon, as a weapon against slicing leather armor, as a weapon slicing metal armor, as a weapon piercing straight through armor.
https://www.youtube.com/watch?v=EDkoj932YFo
the "myth" of the katana is surely romanticized and exaggerated, yet those playing down the quality of the sword have under estimated the superior metalurgic qualities the katana enjoyed.
In any event, though current technology with swedish powdered steel might produce a blade with over all better qualities then produced for the samurai, the skill making the weapon and tool was and is wonderful