  Finding the shortest travelling tour of vehicles with capacity k from the
depot to the customers is called the Capacity vehicle routing problem (CVRP).
CVRP plays an essential position in logistics systems, and it is the most
intensively studied problem in combinatorial optimization. In complexity, CVRP
with k $\ge$ 3 is an NP-hard problem, and it is APX-hard as well. We already
knew that it could not be approximated in metric space. Moreover, it is the
first problem resisting Arora's famous approximation framework. So, whether
there is, a polynomial-time (1+$\epsilon$)-approximation for the Euclidean CVRP
for any $\epsilon>0$ is still an open problem. This paper will summarize the
research progress from history to up-to-date developments. The survey will be
updated periodically.
