Shaw obtained stories from some of the leading writers of the day, including Brian Aldiss, Isaac Asimov, and Robert Sheckley, but the material was of variable quality.

Five volumes were published between 1970 and 1973, edited by Robert Hoskins; a sixth was prepared but withdrawn after Lancer ran into financial problems at the end of 1973.

World War II and its attendant paper shortages led to the demise of several titles,[3] but by the late 1940s the market began to recover.

[5] In 1954, Irwin and Helen Stein started a publishing company, Royal Publications, and launched two magazines, Celebrity and Our Life, edited by Larry Shaw.

[13] Shaw knew the science fiction field well, and was friends with many established writers,[14] so he was occasionally able to acquire good stories.

[5][15] "The Star", which won the Hugo award for that year's best short story,[5] had originally been submitted to The Observer in the UK for a short-story contest, but did not win any of the prizes.

[16] Harlan Ellison's first science fiction sale, "Glowworm", appeared in the second issue,[17] and Shaw was able to publish much early work by Robert Silverberg.

[18] Shaw was able to obtain material by established writers such as Isaac Asimov, Robert Sheckley, Lester del Rey, Algis Budrys, and Jack Vance, though in the opinion of science fiction historian Joseph Marchesani these stories were in many cases not among the authors' best work.

[13] Silverberg and Barry Malzberg had stories in each of the five volumes, and other contributors included established names such as Poul Anderson, Gordon R. Dickson, and Clifford D. Simak, along with newer writers such as Ed Bryant and Dean R.

Mike Ashley describes Infinity as "essentially an adventure magazine aiming at a juvenile readership",[22] and Marchesani calls Shaw "an editor of the middle echelon".

[14] David Kyle describes it as "exceptional",[23] and writer and critic Algis Budrys calls Infinity "Larry Shaw's short-lived but immortal magazine".