Graphene is a two-dimensional material having the charge, spin and valley degree of freedom used for information transfer. For spintronics, graphene has emerged as a leading candidate for device applications due to high mobility and ultra-low spin orbit coupling. Also, graphene is an attractive 2D material for valleytronics because valley polarization can be induced by electrical or mechanical tuning. In this review, we focus on the spin and valley transport in graphene. The spin transport properties of graphene are usually studied with nonlocal spin valve devices because pure spin current can be injected into graphene and be detected as electrical voltage. The electrical generation of a spin current in graphene was tried using the spin Hall effect. The valley transport in graphene is also possible when the inversion symmetry of graphene is broken by applying gate voltage or using bi-layer graphene. From these transport properties in graphene, we briefly introduce the research trends of a spin relaxation mechanism, the spin Hall effect and the valley Hall effect in graphene for spintronics and valleytronics with their applications.