The origin，equivalent forms，and existing partial results concerning Hadwiger’s covering conjec-ture，which is a famous open problem that has lasted for nearly 60 years from convex and discrete geometry，are re-viewed． Ｒelated research problems and corresponding results are also presented． It is shown that，on the one hand，Hadwiger’s conjecture is still a very hard open problem，andon the other hand，there are a lot of fundamental re-searches to be done concerning this conjecture and problems related to it．