The Japanese use hiragana, katakana and kanji. Romaji is what we use - it's basically a way for us to write out the pronunciation of Japanese words.
Hiragana is used for writing out Japanese words phonetically, katakana is used for writing out foreign words phonetically, and kanji are symbols that represent ideas (and can be pronounced different ways).
The Japanese will often mix all three alphabets in one sentence.
For example: パンを食べる。
パン (pan) = "bread," katakana
を (wo) = object particle, hiragana
食べる (taberu) = "to eat," 食 (ta) is a kanji, べる (beru) are hiragana