time distinctions

A Chinese-American told me once that Chinese (Mandarin?) doesn't have
verb tenses.  Is this true?  I can see a language getting by using
circumlocutions or something to indicate time.  I've been thinking of
doing that with Aragis.

What kinds of time distinctions *can* you make?

past
present
future

Maybe all, maybe only one or two.  Who knows?

Various things like progressive, imperfect, perfect, etc.  (Do they count
as time distinctions?)

Maybe narratives and historicals go in here, too?  I've wanted to include
a "legendary" tense in Chevraqis, which indicates something that
"took/takes place" in a legendary context, so you'd use it when speaking
of folklore (Tyl Eulenspiegel's exploits?) or legends (Niebelungenlied?
creation myths?) or prophecies (the Book of Revelation?  Götterdämerung?
and I *know* I misspelled that somehow).  But then I'm not sure if it'd
count as a tense.  (wistfully)  It'd be *fun* if I knew it were allowable.

Thoughts?

YHL