The 1950s magazine Galaxy featured stories by Heinlein, as well as Ray Bradbury and Theodore Sturgeon. Herbert Rossoff believed that if he joined the magazine it would "complete" the lineup. (DS9: "Far Beyond the Stars")
In 1966, Robert Heinlein was invited, by Gene Roddenberry, to write for Star Trek: The Original Series. Heinlein turned down the offer, though. (These Are the Voyages: TOS Season One, Chapter 1: "The Creator") At the time, Heinlein was considered one of the "Big Three" of science fiction authors, alongside Isaac Asimov and Arthur C. Clarke, the latter two known as staunch supporters of Roddenberry's creation. Invited by Asimov to tag along, Heinlein did attend the 1976 "Bi-Centennial-10 Star Trek Convention" at the Hilton Hotel in New York City. 
A photograph of a raktajino bottle seen in The Art of Star Trek shows a label identifying the beverage as imported by Harcourt Mudd and bearing the slogan "Made from The Green Hills of Earth", the title of one of Heinlein's works.
The tribbles are similar to the "Martian Flat Cats" in Heinlein's novel The Rolling Stones, which made the producers of "The Trouble with Tribbles" nervous about a possible lawsuit. Finally, they phoned the author, who was satisfied with a simple "mea culpa" from Gene Roddenberry. (Inside Star Trek: The Real Story, pp. 333-334)
Heinlein invented the verb "grok" (roughly meaning: to completely and totally understand), used in his novel Stranger in a Strange Land. "I grok Spock" was a popular t-shirt and bumper sticker slogan used by Trekkies in the 1970s.
According to the Star Trek Encyclopedia (4th ed., vol. 1, p. 332), the birth and death years of Robert Heinlein were 1907 and 1988, respectively. The authors of this reference work noted that Heinlein was sometimes known as the "Dean of science fiction" because of his role in developing the genre into a sophiscated mode of literary expression. In a note to the entry about this author, it is stated, "Many students of science fiction have regarded Heinlein's works as being a significant influence on Gene Roddenberry's development of the original Star Trek television series."