Worth to note, you will probably use those lots more than in similar concepts in relational world (composite keys).
Example - suppose you have to find last N users who recently joined user group X. How would you do this efficiently given reads are predominant in this case? Like that (from offical Cassandra guide):
CREATE TABLE group_join_dates (
groupname text,
joined timeuuid,
join_date text,
username text,
email text,
age int,
PRIMARY KEY ((groupname, join_date), joined)
) WITH CLUSTERING ORDER BY (joined DESC)
Here, partitioning key is compound itself and the clustering key is a joined date. The reason why a clustering key is a join date is that results are already sorted (and stored, which makes lookups fast). But why do we use a compound key for partitioning key? Because we always want to read as few partitions as possible. How putting join_date in there helps? Now users from the same group and the same join date will reside in a single partition! This means we will always read as few partitions as possible (first start with the newest, then move to older and so on, rather than jumping between them).
In fact, in extreme cases you would also need to use the hash of a join_date rather than a join_date alone - so that if you query for last 3 days often those share the same hash and therefore are available from same partition!