Judith Merril was an established novelist and short story writer, with titles like Shadow on the Hearth and "That Only a Mother", when she launched her annual Year's Best S-F series in 1956. The first volume has an introduction by Orson Welles, and most volumes conclude with a summation of the year's S-F and a list of honorable mentions. Merril pointedly used the abbreviation S-F to mean science fiction, or science fantasy, or speculative fiction, and as the series went on her purview expanded to include selections from non-genre magazines and books. A 13th volume was announced but never published. The "Best of the Best" volume, despite the timing of its publication, includes selections only from the first five annual volumes.
The photo shows (used) paperback reprints of the 12 annual volumes, and the hardcover first edition of the "Best of the Best" volume.
Most-reprinted authors: J.G. Ballard and Fritz Leiber (10 each), then Brian W. Aldiss, Isaac Asimov, and Zenna Henderson (6 each).
S-F: The Year's Greatest Science Fiction and Fantasy, (Gnome, 1956)
[isfdb]
SF: '57: The Year's Greatest Science Fiction and Fantasy, (Gnome Press, 1957)
[isfdb]
SF: '58: The Year's Greatest Science Fiction and Fantasy, (Gnome, 1958)
[isfdb]
SF: '59: The Year's Greatest Science Fiction and Fantasy, (Gnome, 1959)
[isfdb]
The 5th Annual of the Year's Best S-F, (Simon & Schuster, 1960)
[isfdb]
The 6th Annual of the Year's Best S-F, (Simon & Schuster, 1961)
[isfdb]
The 7th Annual of the Year's Best S-F, (Simon & Schuster, 1962)
[isfdb]
The 8th Annual of the Year's Best S-F, (Simon & Schuster, 1963)
[isfdb]
The 9th Annual of the Year's Best S-F, (Simon & Schuster, 1964)
[isfdb]
The 10th Annual Edition of the Year's Best S-F, (Delacorte, 1965)
[isfdb]
The 11th Annual Edition of the Year's Best S-F, (Delacorte, 1966)
[isfdb]