A lubricant composition comprises a base oil and a viscosity modifier including an ethylene/.alpha.-olefin interpolymer. The ethylene/.alpha.-olefin interpolymer is a block copolymer having at least a hard block and at least a soft block. The soft block comprises a higher amount of comonomers than the hard block. The block copolymer has a number of unique characteristics disclosed here. Such block copolymers offer the possibility of improved low temperature performance and flexibility in formulating motor oil, gear lubricants and greases, etc.