A unitary graphene layer or graphene single crystal containing closely packed and chemically bonded parallel graphene planes having an inter-graphene plane spacing of 0.335 to 0.40 nm and an oxygen content of 0.01% to 10% by weight, which unitary graphene layer or graphene single crystal is obtained from heat-treating a graphene oxide gel at a temperature higher than 100° C., wherein the average mis-orientation angle between two graphene planes is less than 10 degrees, more typically less than 5 degrees. The molecules in the graphene oxide gel, upon drying and heat-treating, are chemically interconnected and integrated into a unitary graphene entity containing no discrete graphite flake or graphene platelet. This graphene monolith exhibits a combination of exceptional thermal conductivity, electrical conductivity, mechanical strength, surface smoothness, surface hardness, and scratch resistance unmatched by any thin-film material of comparable thickness range.