In a world of terrifyingly serious news, the opening of the Royal Ballet season with Frederick Ashton's pastoral frolic La Fille mal gardée might seem like a wanton disregard for reality, like a brass band playing "Oh I do like to be beside the seaside" as the Titanic goes down. But that is to misunderstand the reason Fille is so beloved is that it has at its heart a perfectly serious and realistic topic: young love.

The Flames of Paris, in Alexei Ratmansky's 2008 reworking, is a ballet of contrasts. Between the first and second acts, so different in pace and quality, between the naturalistic intimacy of certain pas de deux and the stylised posturing of the crowd scenes, between the tedious masque in Act I and the fireworks show-off variations in Act II, between the liquid velvet blood-red curtains and the flat black-and-white line drawing sets.

What do women want? Ballet plots are not the best guide, since the main desiderata – a well-paying job, coffee dates with girlfriends, not to die young of a broken heart – are rarely the lot of ballet heroines. Comedies at least tend to have the not-dying part covered, but they often fall down on at least one of two other big requirements: that one's family should be supportive, and that one's romantic partner should not be a chump.

"If you know anything about dance," I was told last night by an aged balletomane at the Royal Opera House, "you know that Russian ballet companies are the best." If this is true then the Bolshoi Ballet, biggest of the Russian companies, in Swan Lake, that most quintessential of ballets, must be awe-inspiring.

Exactly 60 years have passed since this company made its first London visit, an unlikely triumph of art over geopolitics. For 1956 was the year Britain was rocked by the Suez crisis and the year the Soviet Union invaded Hungary. British spies Burgess and Maclean had surfaced behind the Iron Curtain after five years on the run and distrust between London and Moscow was acute. Until their plane landed, it was touch and go that the Bolshoi’s London season would happen at all.

Does Alexei Ratmansky, former Bolshoi director and current world-leading classical choreographer, really love Prokofiev's Cinderella, or did he choose to create a new one for Australian Ballet in 2013 principally because he wasn't happy with his first (for the Mariinsky) in 2002? My bet is a bit of both: the second production, like the first, shines with an unfeigned affection for both score and story, but it also reads as a candy-coloured riposte to the usual adjectives applied to the 2002 production: ugly, spiky, uneven.

Graeme Murphy's 2002 Swan Lake for Australian Ballet stitches together plot elements from Swan Lake, Giselle and Lucia di Lammermoor, among other things. No bad thing, that; such mash-ups can work well (see Moulin Rouge), and Matthew Bourne proved way back in 1995 that Swan Lake's story can be totally reconfigured and still work gloriously (we do not talk about the 2011 film Black Swan).

Why does Natalia Osipova, one of the world's best classical, dramatic ballerinas, want to start a sideline in contemporary dance in the middle of her career? Two years ago, when she mounted her first self-commissioned contemporary triple bill with her then newly-ex-fiancée Ivan Vasiliev, I was willing to believe that it was for the love of trying new things, pushing her own boundaries, and taking all aspects of her artform seriously.

I could tell you what the German word "Betroffenheit" means by giving a dictionary definition, etymology and connotations and so on. But I won't, because this dance-drama hybrid by Jonathan Young and Crystal Pite is precisely not about pinning down definitions or making sense through words in a descriptive, iterative sort of way, but about capturing feelings or states of being in a much more metaphorical, experiential, immersive way. Betroffenheit is in one sense, then, the feeling you have after watching the show Betroffenheit.

It shows you just how much Kenneth MacMillan changed ballet in this country that 1960's The Invitation, with its onstage rape, sexual grooming and child abuse, can act as the reassuring classic at the heart of the new Royal Ballet triple bill which opened on Saturday.