One thing to listen for in Shostakovich's music is his four-note musical monogram:
/\
------||-------------- /-\---------------------+
/ / \ b | | ||
-----/|------|--------|\_/---- /-\------------+|
/ | |\_/ | | | / \ ||
---/--|------|--------|-------|\_/----|-------+|
| /|\ | | | |\_/ ||
---\-\|-\----|--------|-------|-------|-------+|
\ | / | | | ||
-----\|/-----|----------------|-------|--------+
| |
/
In abc notation:
X:1
T:DSCH monogram
C:Dmitri Shostakovich
L:1/4
M:C
K:C
d _e c B|]
How do you get from "Dmitri Shostakovich" to the sequence of notes above?
Shostakovich's monogram is reminiscent of J. S. Bach's musical signature B A C H =B-flat A C B-natural. Good places to listen for the D S C H theme are in movements 3 and 4 of Shostakovich's Tenth Symphony (opus 93), in the second movement of his first Violin Concerto (opus 99), and in the Eighth String Quartet (thanks to freshmint for pointing out this last example).
And, for a rather different use of the same motif, see spiregrain's excellent writeup on Benjamin Britten's Rejoice in the Lamb.