The present invention provides a copolymer of a conjugated diene compound and a non-conjugated olefin that is used for manufacturing a rubber excellent in crack growth resistance, heat resistance and ozone resistance and that includes a cis-1,4 bond at a unit derived from the conjugated diene compound, a rubber composition containing the copolymer, a rubber composition for tire treads using the rubber composition for tire tread members, a crosslinked rubber composition obtained by crosslinking the rubber composition, and a tire using the rubber composition or the crosslinked rubber composition. In the copolymer of a conjugated diene compound and a non-conjugated olefin, the cis-1,4 bond content of a unit derived from the conjugated diene compound is more than 92%.