Fig.: to stay up very late at night working or studying

The official presentation of my project is due tomorrow and I'm sure I will burn the midnight oil tonight checking every single line of the report

La presentazione ufficiale del mio progetto è domani mattina, perciò di sicuro farò le ore piccole per controllare ogni singola riga del rapporto

The anatomy exam is coming up and I'm not ready. I think I'll have to burn the midnight oil every night and forget about friends and pubs

L'esame di anatomia si avvicina e non sono pronto. Penso che dovrò fare le ore piccole tutte le sere, altro che amici e pub

This expression goes back to the days when lamps were lighted by oil, so if you were burning the midnight oil, you were up late working or reading by the light of an oil lamp