At first glance, Caroline Cahoon’s strikingly chic poster of a mysterious young woman with angry, piercing eyes — and no mouth! — looks like a dazzling vintage illustration for Bergdorf Goodman, or maybe a tear sheet from a bold new Pucci campaign. But her mod artwork turns out to be for a small production of the musical “Carrie” in Grand Rapids, Mich.

I wanted to frame the piece and hang it in my home. I also wanted to hop on a plane to see the show.

That’s what great theater posters do: sell by design. Whether it’s the sexed-up photograph of Neil Patrick Harris on Broadway or the pared-down treatment of a domestic drama in a regional theater, the best posters convey the conceptual complexities of the plays they serve. Spirited or reserved, these six images — my 2014 favorites — demonstrated a keen sense of both style and salesmanship. Following are edited excerpts from conversations with their creators.