One of the frequently asked questions about the Hungarian Opera House in Budapest is if it is open in summer time, if there are any performances in June, July and August. The short answer is that the building of the Hungarian State Opera House is open, and open for guided tours, but there are no performances (every summer, 3 times a week some of the Opera House artists perform on the Budapest Opera and Operetta Cruise).
If you love operas, and insist on the Opera House venue, we have bad news: the opera season in Budapest usually finishes around late June or early July, which means that you may very well find some operas and ballets in June, which are worth seeing, then the season starts late September again. You can check if there are other venues in Budapest where operas can be seen (live and virtual real time screenings).
That said, the building of the Opera House is open for tourists all summer (see more info about the Budapest Opera guided tours here), even if there are no opera performances or very few surprising ones, like in 2012 the Chinese guest performance early July.
In other words, the Opera House welcomes tourists for guided tours starting each day, from Monday to Sunday at 3 pm and at 4 pm.
If you are interested in one of the best European opera performances, see the current dates in Italy, France, Germany, the United Kingdom, Austria, etc.
See more guided tours in Budapest here.