Father's Day is held on the third Sunday in June in the UK, so this year it will be on 16 June.
Unlike Mother's Day or Mothering Sunday, which is an old traditional festival originating in the UK, Father's Day is a modern one. It started in the United States, and while several people may have been involved in getting it started, credit for founding the modern Father's Day is usually given to Sonora Smart Dodd from Arkansas. Smart Dodd had been impressed by the Mother's Day celebrations (although these go back hundreds of years in Europe, in the US it only began to be celebrated around the beginning of the 20th century) and as she was very close to her own father she thought fathers should have a festival of her own. So on 19 June 1910 she organised the first Father's Day celebration, in Washington (it was the nearest possible date to her father's birthday). It became popular and eventually spread around the world.