It is well-known and traditional that symphonies, concertos, sonatas, and so on, consist (in general) of multiple movements. The styles and tempos of each of these is often conventional, for example starting with a dramatic and impassioned first movement, with a slow movement in the middle, and finishing with a bombastic finale.
But apart from adhering to the above structure (and a lot of the time such compositions actually don't), and apart from the fact that they are often in the same key (although not necessarily so), it is vanishingly rare for there to be a common musical theme running all the way through each of the movements. In fact, beyond the fact that they are intended to be played as a single suite, and hence heard all as a single suite, there appears to be no direct musical connection to the movements at all.
In my formal music classes at school, no insight was given into the analytical structure of, for example, a typical symphony, beyond the above observation of the fact that the movements are grouped together. I have explored my way through a fairly wide selection of the classical legacy: symphonies, concertos and sonatas, from Bach and Haydn to Shostakovich and Brian, and I have never been able properly to identify a "unifying" theme through any -- apart from some operas and ballets and more obviously programmatic music (e.g. Prokofiev's Romeo and Juliet; Walton's Belshazzar's Feast; Vaughan Williams's Job, etc.)
So: apart from the fact that they were intended to be grouped together by diktat of the composer, what does glue the movements of a symphony / sonata / concerto together?