Big lizard go boom! That, of course, is the basic appeal of Godzilla, the prehistoric creature stomping on multiplexes, making the box office go ka-ching.

But fans know that the full story, stretching back seven decades to the A-bombs of World War II, is rather more complicated. Indeed, the new American “Godzilla,” although it cost Warner Bros. $160 million, can’t help looking like a preschooler’s windup toy compared with the two dozen or so Japanese films that constitute the beast’s true legacy.

Staples of Japanese pop culture (not to mention “Mystery Science Theater”), the Godzilla movies made from 1954 to 2004 comprise three distinct cycles and run the gamut from sublime to silly, terrifying to terrible. The best ones — such as the very first, 1954’s grimly walloping “Gojira” (free on Hulu Plus with subscription) — are more than merely fun as they wrestle with the horror of nuclear warfare, the fragility of man-made superstructures and the vengeful power of nature. These are movies for doomsday times, then and now.

Those of a certain age will remember the early films fondly from Saturday matinee screenings and TV broadcasts of the ’60s and ’70s. Running often enough to break in the projector was 1965’s tag-team smackdown “Godzilla vs. Monster Zero” (free on Netflix with subscription or Amazon Instant Video with Prime), wherein the lizard king, along with pterodactyl Rodan, travels through outer space to fight his archenemy, the three-headed Ghidorah. Boasting miniatures and men in rubber suits, the FX are cheesy and honorably old-school.

A city-squashing nightmare at first, the big guy had become downright cuddly by ’67, as films such as “Son of Godzilla” and “Godzilla’s Revenge” (Netflix and Hulu Plus) — both with the insufferably Barney-like Minilla — discovered the virtue of exploiting kindergartners. Still, 1971’s antipollution tract “Godzilla vs. the Smog Monster” (Hulu Plus) skewed to older kids with its psychedelic images and practically narcotic narrative.

As if passing the movie-monster crown to the shark of “Jaws,” the so-called Showa series of badly dubbed ’Zilla pictures ends in the mid-’70s, the wacky “Godzilla vs. Mechagodzilla” (Vudu for purchase only) directly preceding the ferocious “Terror of Mechagodzilla” (Netflix, Amazon). Both of these anti-technology epics are awesome, although many fans swear by the superiority of the subsequent Heisei series of the ’90s, particularly “Godzilla vs. King Ghidorah” (for purchase only on Google Play and Amazon) and “Godzilla vs. Destoroyah” (ditto), the latter featuring the reptile’s sad demise.

R.I.P., Godzilla — at least until the next sequel.

Also notable on VOD

Moving from the gargantuan to the minuscule, we find “Double Play: James Benning and Richard Linklater” (now on iTunes, Vudu and Amazon), critic-turned-documentarian Gabe Klinger’s suitably laid-back ode to the indie filmmakers of the title. In purely economic terms, the experimental Benning (“One Way Boogie Woogie”), a native of Milwaukee, makes the modest Linklater (“Before Midnight”) look like Godzilla, but Klinger’s film reveals the two friends as equals in their philosophical approaches to the craft — and their kindred love of baseball.

Like Linklater’s movies, including the soon-to-be-released “Boyhood,” “Double Play” is loaded with thought-provoking dialogue, including meditations on time, relationships and the challenges of staying true to one’s artistic muse. It’s the sort of conversation one periodically finds onstage at the Walker Cinema, but hardly ever in movies.