God-sent sea monsters and divinely ordained human sacrifices don’t wash well with opera updated. The favoured contemporary take on the post-Trojan War myth of Mozart’s Idomeneo, which may even have originated in the last Covent Garden production 25 years ago by a fitfully brilliant Johannes Schaaf, has been to put a populace at risk from natural disaster and pestilence. Clearly the programme was expecting something of the sort, with its images of Hurricane Katrina. But no, for director Martin Kušej, the only monster is the state.

Madness is a favourite trope of opera, less so of ballet. There’s Giselle, but her insanity lasts only a few minutes. There’s Kenneth MacMillan’s delusional Anastasia, who believes she's the daughter of the last Tsar of Russia, but the advent of DNA testing destroyed the story’s credibility.

This morning, those who follow ballet on both sides of the Atlantic might be feeling a bit like the male soloists at the beginning of Ashton’s Scènes de Ballet: turning their heads sharply, almost pantomimically, from side to side. Over there, in New York, Wendy Whelan, the prima ballerina retiring after a 30-year career with City Ballet, made her farewell in a programme heavy on modern masters Wheeldon and Ratmansky, including a world première.

Even before I stepped into the Royal Opera House, it was clear to see that it had been transformed for the opening performance of Mark-Anthony Turnage’s Anna Nicole. A red carpet outside; the pervasive smell of popcorn within; the stage curtains, usually red, now a gaudy shade of purple: the opera house clearly had a case of All Things American.

The Royal Opera House is on fire this month. Not literally (unless someone knocks over the flaming braziers outside) but with the varied illuminations of the Deloitte Ignite Festival, co-curated by the Royal Ballet and Minna Moore Ede of the National Gallery. The theme this year is Myth, and specifically Leda's rape by Zeus in swan form, and Prometheus's gift of fire to humanity.

This was the most eagerly anticipated programme of the Mariinsky visit - something old, something borrowed and something new. The old, that colourful fairytale of Stravinsky’s lush, melodious youth, The Firebird; the new, a recent acquisition by the Londoners’ favourite Russian, Alexei Ratmansky; and the borrowed, something from English ballet legend, Frederick Ashton’s Marguerite and Armand, once kept under glass with the Fonteyn and Nureyev myths, but eventually released from the museum by Sylvie Guillem and Nicolas Le Riche a decade ago.

The ballerina claque wars that generally accompany visits here by the Mariinsky Ballet are raging particularly feverishly this year, but it all falls silent when Uliana Lopatkina makes one of her increasingly rare appearances. So much noise is focused on legginess or hip flexibility of these size-zero ballerinas, and yet the Mariinsky knows more than any other company in history that it is not body but mind that matters in the final analysis. Their luminous historical legend Galina Ulanova was nothing to look at physically, until she started dancing.

Can it really be 12 years since Antonio Pappano inaugurated his transformative era as the Royal Opera’s Music Director conducting Strauss’s Ariadne auf Naxos? Christof Loy’s production seemed so radical at the time.

Puccini’s racy first masterpiece, like its successor La bohème, should feel like an opera of two halves – the first full of youthful exuberance, the second darker and ultimately tragic. The contrast here, alas, was between vivacious performers and a sombre, sometimes confused updating by Jonathan Kent which too often dwarfed or zapped their better efforts.

The big message of The Woman Without a Shadow, brushing aside the narrower, moral majority preaching that you’re incomplete without children, seems clear: fulfillment can’t be bought at the cost of another’s suffering. Yet the path towards that realization in this "massive and artificial fairy-tale", as an increasingly alienated Richard Strauss called it, is strewn with magnificent thorns in both his complex, layered music and Hugo von Hofmannsthal’s elaborate symbolic libretto.