  This survey reviews some of the most recent achievements in the saga of the
axiomatisation of parallel composition, along with some classic results. We
focus on the recursion, relabelling and restriction free fragment of CCS and we
discuss the solutions to three problems that were open for many years. The
first problem concerns the status of Bergstra and Klop's auxiliary operators
left merge and communication merge in the finite axiomatisation of parallel
composition modulo bisimiliarity: We argue that, under some natural
assumptions, the addition of a single auxiliary binary operator to CCS does not
yield a finite axiomatisation of bisimilarity. Then we delineate the boundary
between finite and non-finite axiomatisability of the congruences in van
Glabbeek's linear time-branching time spectrum over CCS. Finally, we present a
novel result to the effect that rooted weak bisimilarity has no finite complete
axiomatisation over CCS.
