The history of the underground press includes some areas that I consider pertinent in relation to zines from the '80s.
First of all the underground press, was indeed just that, a press (albeit an alternative one). Many of its publications utilized newsprint formats, and offset printing techniques, with the printing runs measuring in the thousands rather than in the hundreds. While much of the work in putting together the papers could be done in peoples' homes, studios and apartments, the final production invariably involved being taken out of the living situation and out to the printers.
The number of people involved in gathering information, writing articles, and generally coordinating the production of an issue was significantly more than the equivalent number involved in artists' self-publishing. The impetus and idealism that fueled the underground press was the goal of providing another voice, one which was a partisan viewpoint for the emerging counter culture, and its opposition to the corporate and establishment media.
The underground press was just one part of the matrix that constituted the so-called counter culture. With its antecedents in the mid-50s it would spring to full force by the early sixties, fanned by a generation of youth not willing to accept the social, political and cultural status quo. Drugs, rock music, the war in Vietnam, and racial inequality were just part of the volatile mix that would alienate many from the dominant 'establishment' culture, into the search for and the construction of, a more authentic culture that reflected the concerns of this generation in revolt.
The underground press played an important part in speaking for and networking these disparate groups across the country. The rapid increase in the numbers of alternative newspapers (nationally and internationally), as the decade wore on, provides clear evidence of the vital part they played in disseminating information and ideas, and linking communities who subscribed to common ideals.
Towards the end of the '60s and into the early '70s as the counter culture loses its earlier coherence, there's a noticeable move towards underground newspapers concerning themselves with the issues of particular communities, both geographically and interest wise. This had happened before, but with the increased fragmentation of the counter culture, local concerns took on a new importance.
In England this can be seen more clearly with the rise of community presses, as collectives formed within the cities and groups decamped into the country. Community presses engaged and mobilized around issues that affected their immediate community, within a broader web of national and oppositional media.
The pertinent points from the experiences of the underground press and the counter culture in general and their relevance to zines in the 80's can be stated by the following:

• In combination with the underground press the youth movement had decisively carved out an arena of social space within the larger culture that they could claim as their own, a counter culture or a parallel culture that offered an alternative to the dominant values of the establishment.
  
• Music played a vital part in delineating the territory of the counter culture and indeed might be defined as one of the rallying points of the broader cultural opposition.
  
• Drugs and their influence on the artistic output of this period cannot be underestimated in delineating a break with previous visual conventions.
  
• Closely connected to the above is the renaissance of poster art for music events (closely related to this would be designs for LP covers), and coupled to these two vigorous emerging visual forms are the political graphics and posters of this period.
  
• As in many areas of the counter culture, old conventions were discarded as new solutions attempted, this is nowhere more clearly seen in the layout, design and typographic experimentation that took place within the pages of the underground press.
  
• And finally the importance of the underground press in helping to create, by disseminating visual and written material that helped foster, sustain and network an international movement, and in some of its later manifestations to play an active and participatory role within specific local communities.