In the UK, a secondary school taking pupils between the ages of 12 and 18. Following various educational reforms, schools called "grammar school" fall into all kind of private and state-run categories, but used generically the term refers to local-authority-run schools which operate a selective intake system, traditionally via the "eleven plus" or "twelve plus" exam, which creams off the most academic 10% or so of pupils into grammar schools and decants the rest into secondary modern schools. Since the 1970s in most parts of the UK this system has been replaced by a non-selective "comprehensive" education system which doesn't actually write off 90% of the population's life chances at age 11. Selective state schooling continues to operate throughout the counties of Kent and Buckinghamshire and in smaller areas elsewhere for a total of around 150 schools.
NB that in the UK "High School" is generally a synonym of grammar school, especially but not exclusively used for single-sex selective schools for girls; many of the oldest established boys' grammar schools had parallel girls' high schools set up this century (e.g. the independent Manchester Grammar School and Manchester High School).