clj-time is a wrapper around Java Joda-Time.
If you use Leiningen or Maven, you can add it to your project via Clojars.
There are lots of samples on the GitHub page which show how to do date arithmetic and parsing/formatting. For example:
(in-minutes (duration (date-time 1986 10 2) (date-time 1986 10 14)))
;; gives 17280
(def custom-formatter (formatter \"yyyyMMdd\"))
(parse custom-formatter "20100311")
;; gives #<DateTime 2010-03-11T00:00:00.000Z>
(unparse custom-formatter (date-time 2010 10 3))
;; gives "20101003"