WHAT ABOUT NOWADAYS?
Today Spanish is said to be the only language using such upside-down marks! There are some other languages using ¡ and ¿ which are related to Spanish culture, though.
Is it possible to write a question in Spanish with only one punctuation mark at the end of the sentence? Yes, but only in messages and other social media websites (that is, in everyday life), since people tend to be lazy to add one more sign in the beginning of a sentence :) However, in books and newspapers, for example, ¡ and ¿ are always present.
WHEN IT ALL STARTED
You may ask: how did these upside-down punctuation marks even appear? Well, these inverted marks were offered by the Royal Spanish Academy which published the 2nd edition of the "Ortografía de la lengua castellana" in 1754. To be precise, at first the question mark "¿" was offered to appear in usage (and it took quite long to be adopted) and after some time the "¡" was added as well.