Lucille Ball and Desi Arnaz built an entertainment empire. Against all expectations and rather stiff odds, the married pair not only had the top-rated TV series in “I Love Lucy” to their credit but also Desilu Productions, which produced many of the most popular series of the day, including “Mission Impossible” and Ball’s own “The Lucy Show.” The pair enjoyed great success in Hollywood and no small amount of wealth.

But behind the scenes, all was not well, as Amy Poehler unveils in the new documentary “Lucy and Desi,” premiering Friday on Amazon Prime. Though Ball and Arnaz enjoyed a fairy-tale romance and achievement beyond imagining—particularly for Arnaz, a Cuban immigrant who spoke no English when he arrived in Miami—offscreen the pair couldn’t get along, perhaps at least partially due to the fact that Ball’s success began to eclipse her husband’s. “Lucy and Desi” attempts to deal with such psychology, and the couple’s daughter Lucie discusses awkward family vacations they undertook in attempting to save the marriage.

The documentary is at its best when demonstrating how Ball refused to be spoken down to by a male-dominated Hollywood elite. Rather than have power taken out of her hands, she used Desilu Productions to produce her own shows—leaving the men out of the decision-making process, and becoming a one-woman mogul until, late in life, she agreed to sell the studio to Paramount.

That this contributed to her marriage to Arnaz crumbling seems to be in little doubt, even though the pair nonetheless continued to love one another the rest of their lives, and long after they had both remarried.

This is one of the 20th century’s great love stories, and demonstrates how Ball and Arnaz were not only partners in life but in business. Their chemistry was real, even as their marriage fell apart, and millions of Americans got to enjoy their banter on a weekly basis. We are reminded that in those days, there were no second takes as “I Love Lucy” went out over the air as it was, warts and all—-much like the amazing couple at its center.

Available on Amazon Prime starting today