Contemporary pop songs are usually based on four chords that are looped continuously, and these chord progressions very often come from the circle of fifths.

In any major key the circle of fifths progression is I IV vii° iii vi ii V I.
The well-known vi – ii – V – I is the tail of that progression. This four chords progression can be rotated to produce other popular variants: I vi ii V (the doo-wap progression) and ii V I vi.

Another popular progression that comes straight from the circle of fifths progression is iii vi ii V, which can also be rotated to produce ii V iii vi for example.

Not to mention the ii V I progression that is everywhere in jazz.

But not all chord progressions come from the circle of fifths.
Another popular way of building chord progressions is by using what is called harmonic sequences.

Here is the chord progression of the chorus of the well-known song “Hotel California” by the Eagles:
|Bm – – – |F#7 – – – |Asus2 – – – |E9 – – – |
|G – – – |D – – – |Em7 – – – |F#7 – – – |

There are several transitions that don’t seem to make much sense in that progression (can you see which ones?). And yet the chorus seems to “work”…

This is a typical example of an harmonic sequence. The chords Bm to F#7 are linked by an ascending fifth (or descending fourth), and so are the chords Asus2 – E9 and G – D. Now, A is a whole step lower than B, and G is a whole step lower than A. And that’s the pattern, or “sequence”.
The end of the progression is simply iv V7 leading back to i.

So, whenever a chord progression doesn’t seem to make sense, check to see if it is some sort of harmonic sequence.