(written from a Production point of view)
The Inside Star Trek magazine was the first "official" fanzine, distributed through the first officially authorized fan club for the Star Trek franchise, the Star Trek Interstellar: The Official Star Trek Fan Club. The magazine was published from 1968 through 1969, while the third season of Star Trek: The Original Series was in production.
Strictly speaking, neither fan club nor magazine was endorsed nor authorized officially, as the latter was not published under the auspices of the Paramount Publicity Department, the legal owner of the Star Trek brand, but rather by the privately-operated "Star Trek Enterprises", the short-lived, original name of Gene Roddenberry's merchandise company Lincoln Enterprises. However, the studio at the time was not in the slightest interested in their recent Star Trek purchase, and was actually looking for ways to cancel the series. As a result, no commercial or publicity activities on behalf of the series were undertaken by the department, and those that had been, such as the free mail-order distribution of publicity photographs to fans, were immediately scrapped upon the acquisition of Desilu Studios by Paramount Pictures in 1967. But, considering the closeness to the actual production of several of its contributors, the magazine, essentially an illegal publication, is for practical purposes, considered "official".
Ruth Berman produced and edited twelve eight-page issues (with the exception of issue 1, which had twelve pages) of Inside Star Trek and enjoyed close access to Star Trek's cast and crew during the production of the series' third season. After Star Trek was canceled by the network in 1969, the club and magazine were discontinued, as a depressed Roddenberry temporarily lost heart over the seemingly failure of his creation. Editor Berman immediately started a new fanzine, T-Negative, that ran for 35 issues from 1969 until 1979. 
Obviously endorsed by Roddenberry, editors were given access to the studio and contributions were made by Roddenberry, D.C. Fontana, John Dwyer, Matt Jefferies, William Theiss, Charles Washburn, Fred Phillips, William Shatner, Leonard Nimoy, DeForest Kelley, James Doohan, Walter Koenig, Nichelle Nichols, and George Takei, among others. Future Star Trek production staffer, but fan at the time, Andrew Probert illustrated a number of covers and some interior art work, as did Gregory Jein. 
Seven years later, in 1976, the magazine was relaunched, following a similar formula. While it was re-titled Star Trektennial News, it continued the numbering where Inside Star Trek had left off, issue 13 being the first one under its new heading. Again published by Roddenberry's company, now as Lincoln Enterprises, it was relaunched in order to keep fans appraised of his efforts to bring back Star Trek as a live-action production, from The God Thing, via Star Trek: Planet of the Titans and Star Trek: Phase II through Star Trek: The Motion Picture. Roddenberry's personal assistant during those years, Susan Sackett, together with Virginia Yable, served as editors for the magazine.
The magazine ran for another eighteen issues, returned to its original title from issue 25 onward, with page count intermittently increasing from 1977 onward as possible productions assumed more substance, and starting to include behind-the-scenes pictures. Publication ceased shortly before the release of The Motion Picture in 1979.
|1968 advertisement for Star Trek Interstellar: The Official Star Trek Fan Club and Inside Star Trek magazine from Star Trek Catalog #1|
|1, July 1968|
|Cover: Rae Ladore
|2, August 1968||Cover: Gregory Jein
|3, September 1968||Cover: N. Criss|
|4, October 1968||Cover: Rae Ladore|
|5, November 1968||Cover: Rae Ladore|
|6, December 1968||Cover: Rae Ladore|
|7, January 1969||Cover: Andrew Probert
|8, February 1969||Cover: Andrew Probert
|9, March 1969||Cover and interior art: Andrew Probert
|10, April 1969||Cover: Andrew Probert|
|11, May 1969||Cover: Andrew Probert
|12, June 1969||Cover: Rae Ladore
|13, May 1976|
as "Star Trektennial News"
|8 pages, cover: G. Boudreau|