In the music video A Casa by Javier Garcia, take a look at two lines of the catchy refrain:
Anoche fue muy fuerte...
Last night was very tough...
Caption 7, Javier García - A CasaPlay Caption
La noche fue muy fuerte...
The night was very tough...
Caption 11, Javier García - A CasaPlay Caption
Note that anoche means "last night." Some non-native Spanish speakers think they should say 'la noche pasada,' but that would be akin to saying "the day before today" when you mean simply "yesterday" in English. So listen closely to distinguish 'la noche' -meaning, more generically, "the night"- from 'anoche' -meaning "last night"- as in this week's featured song.
Here are some more useful Spanish terms for the past:
Dígame... Eh Padre, ¿se acuerda de esa chica que estábamos hablando ayer?
Tell me... Um, Father, do you remember that girl that we were talking about yesterday?
Caption 12, Muñeca Brava - 2 Venganza - Part 2Play Caption
Ayer = "Yesterday"
Anteayer = "The day before yesterday"
You'll note ante means "before," and so anteayer is really just a contraction of "[the day] before yesterday." Following the logic, can you guess what anteanoche means? Yup, "the night before last." (Isn't it convenient to have one Spanish word when in English we require four?)
Moving from days to weeks and years, the rules change a little. You see, there's no single word that means "last week." Instead, you have to say: 'la semana pasada.' And to say "last year," use el año pasado. But there is a word that means "yesteryear": It's antaño. Like "yesteryear" in English, antaño in Spanish refers to "times past"--not necessarily last year.