An adverb indicating that a state is continuing: 'still' or 'as yet' (e.g., 'まだ起きている' = 'still awake').
彼はまだ会社にいる。
He is still at the office.
雨はまだ降り続いている。
The rain is still continuing.
この本はまだ読んでいない。
I still haven't read this book.
Used with negative predicates as 'まだ〜ない' to mean 'not yet' (something expected has not happened yet).
仕事はまだ終わっていません。
The work isn't finished yet.
彼女はまだ帰ってきていない。
She hasn't come back yet.
バスはまだ来ていないから、もう少し待とう。
The bus hasn't arrived yet, so let's wait a bit longer.
Used to intensify a comparison, meaning 'more' or '(more) still'.
練習すればするほど、まだ上手になる。
The more you practice, the better you become still.
その問題は前よりまだ難しくなった。
That problem became even more difficult than before.
Can mean 'at least' or 'relatively/comparatively' in some contexts (e.g., 'まだまし' = 'it's still better').
値段は高いが、まだ品質はいい。
The price is high, but the quality is still good.
まだ小さな問題だから、すぐ直せるだろう。
It's still a small problem, so it can probably be fixed quickly.
Used like a quasi-adjective to indicate something is unfinished or incomplete; the kanji 未だ is sometimes seen in written language.
この建物はまだ工事中だ。
This building is still under construction (unfinished).
計画はまだ途中で、最終案が出ていない。
The plan is still in progress; the final version hasn't been produced.