Darrell D’Silva as Siward in the National Theatre of Scotland and the Royal Shakespeare Company’s production of “Dunsinane.” (KPO Photo)

Macbeth is dead. What’s next? In David Greig’s imaginative and ferociously topical “Dunsinane,” the English army occupies a hostile and internally fragmented Scotland. Faster than you can say “quagmire,” you recognize the saga in terms of our knotty 21st-century conflicts in Afghanistan and Iraq.

This big, bold show is the latest in the valuable and productive partnership between the Shakespeare Theatre Company and the National Theatre of Scotland. The Scottish troupe has twice toured its electrifying contemporary military chronicle “Black Watch” through Sidney Harman Hall, and two seasons ago, its quirky, little ballad-filled “The Strange Undoing of Prudencia Hart” was performed in a small bar off Dupont Circle.

That pub-style whimsy was by Greig, and “Dunsinane” features live music, too — a percussion-drum-guitar trio that underscores action and bridges scenes with crunchy rock riffs. The sudden eruptions of battle and chaos evoke the mayhem of “Black Watch,” yet the diplomacy-minded “Dunsinane” is an entirely different animal.

It starts with Shakespeare, as English soldiers take control of Scotland in the uprising that leaves Macbeth dead. (The Royal Shakespeare Company, which premiered the play in 2010, is a co-presenter of this U.S. tour.) Lady Macbeth — here known as Gruach — lives, and says her son should be king. The English have come to install Malcolm on the throne: Malcolm’s claim is that he is the son of Duncan, the king murdered by the ambitious Macbeth.

You don’t need to know “Macbeth” to keep up, although Greig and director Roxana Silbert do a remarkable job grounding the show in a Shakespearean key that flexibly connects to right now. With its broadswords and chain mail, the look is medieval yet the language is hardly remote. The soldiers swear and yell like modern warriors — “Clear!” they shout once they have secured the castle — and the play’s diplomatic negotiations range from delicacy and elegance to roaring vengeance.

The bargaining sessions are joltingly familiar. England’s occupying force is led by Siward, a brusque but decent military man appealingly played by Darrell D’Silva, and Siward’s dialogues with Ewan Donald’s silky Malcolm are both funny and maddening. Malcolm is set up as England’s puppet, yet Siward can’t quite control the strings. Malcolm’s serene resistance is fascinating: There is so much about Scottish culture that the English can never understand, Donald’s placid Malcolm instructs D’Silva’s blustery Siward. It’s the first thing that begins to thin Siward’s patience.

The second is Gruach, mesmerizingly played by Siobhan Redmond as a proud queen who masterfully exploits her reputation for witchcraft. The way Redmond languidly toys with a naïve young British soldier who believes the worst is one of the show’s nice bits of comic relief, and Redmond’s slow seduction scene with D’Silva’s approachable Siward ripples with the mystery of a strange culture. English is not Gruach’s native tongue, and the queen’s luscious Scottish-Gaelic accent seems as alluring to Siward as her long crimson braids.

But what is Siward trying to accomplish? Greig has the restless soldiers ask it, too, as the mission stretches out and peace prospects between Gruach and Malcolm are sabotaged by Siward’s missteps. Atrocities begin to seem ripped from the headlines as the factions coo together but then storm away, with casualties piling up on the field.

Physically, the production isn’t especially complicated, but Robert Innes Hopkins’s set of ancient-looking castle steps sloping up one side of the stage combines with Chahine Yavroyan’s foggy lighting to create a timeless, menacing atmosphere. (Hopkins also designed the appropriately “Macbeth”-y costumes.) The scale is classical, with acting to match, especially in the majestic, subtle central performances by Redmond, D’Silva and Donald. The rank-and-file are well represented, too, led by Alex Mann as an English lieutenant and Keith Fleming as a formidable Macduff.

Greig has said the 2003 toppling of Saddam Hussein’s statue in Baghdad was among the impulses behind this play, although it also speaks to the recent referendum on Scottish independence (the Edinburgh-born Greig was in favor of breaking away). You hardly need to brush up on your Shakespeare to see that the peacekeeping and nation-building of “Dunsinane” — a welcome return by the National Theatre of Scotland and another triumph of international programming for the STC — has no end of resonance here and now.

Dunsinane

by David Greig. Directed by Roxana Silbert. Composer and sound designer, Nick Powell. With George Brockbanks, Helen Darbyshire, Tom Gill, Toyin Omari-Kinch, Arthur McBain, Matt McClure and Mairi Morrison. About 2 1/2 hours. Tickets: $20-$110. Through Feb. 21 at Sidney Harman Hall, 610 F St. NW. Call 202-547-1122 or visit www.shakespearetheatre.org.