Intervals, keys, chords move in various ways. These are the traditional movement(s), by: 4ths or 5ths, maj or min 3rds, whole or half step up or down (tritone), or chromatically, repectively. This can be accomplished through abrupt or through dominant 7th (or it's variation, mostly by 4th or 5th, or voice leading control, regardless of established harmony).
Most always some portion(s) of the cycle of 4ths and 5ths occur. From Renaissance, Classical, Swing, Bebop, Rock, etc, this formula or idea exists. There are only two chords, in our present system, I and V7. most all tunes, songs, compositions, whatever term, can be boiled down to this constant.