Katanas are a type of Japanese sword, but nowadays the term is internationally used to talk about all Japanese swords in general. They are considered as the best swords ever created, they have a curved shape and they are many different types and sizes.
Strictly talking a katana has around 70 cm, the longest ones are called tachi and were used by cavalry. The short versions are called wakizashi and kodachi, which are equivalent to our daggers. Samurais where equiped with a katana for the face to face fights and a short wakizashi to kill by surprise without being seen.
This is a katana forged 900 years ago by Sanjo Munechika, and is one of the oldest katanas in the National Museum (Ueno Station at Tokyo
It can be appreciated how dedicated, simple and well done were the Japanese tools on those times while at Europe we had huge and rough swords.
Nowadays katanas are created by some artists, people from the Mukansa clan seem to be the best. Two of the Musakansa family members are Living National Treasures selected by the Japanese Government.
If you wanna by a katana, you can find average katanas at some hidden shops at Asakusa (Tokyo). I took one video inside of one of those shops.
Next, some videos were the sharpness of the katana edge can be appreciated.
At this last video there is a little explanation about how katanas are made.