We have a current periodicals display in our main library, but all periodical issues at our main library not bearing the date of the current calendar year are kept in our automated warehouse appended to the building.  Whether we bind a title or not depends on its physical properties, on whether or not archival access is available on JSTOR and whatever funds are available at a given time.  As a rule, we prefer to maintain an archive of newspapers and newsmagazines on film and forego retention of paper and binding.  Titles which can be found on JSTOR we code and put in the warehouse as is and make an appointment to flush them out when they are no longer needed; however, a selection of such titles are unsuitable for coding raw and we put them in archival boxes which are coded and put in the warehouse (and flushed periodically).  We will make use of archival boxes for publications such as the Boston Review, because their dimensions are such that our bookbinder would have to make use of stitch binding.  We make use of adhesive binding (without exception) for user convenience. 
We will also make use of phase boxes if the paper is too brittle to be safely bound.  That is only done for odd retrospective projects, however.  IW