As transistor scaling has slowed down at advanced technology nodes due to physical limitations of silicon based devices, new device structures such as FinFET and ultrathin body (or FDSOI) transistors have been developed to continue improving their performances. Other endeavors include devices using new materials, e.g., two- dimensional (2D) crystal materials. In the past decade, graphene based devices as well as transistors have been a great interest due to its unique electrical, mechanical and optical properties. Along with graphene research, other 2D crystal materials like transition metal dichalcogenides (TMDC), individually or in combination with graphene, have been investigated, showing other intriguing properties. This thesis is based on 2D heterostructure in combination with graphene to understand the physics behind the device in electrical and optical perspectives. The first theme of the thesis is electrical characteristics of MoS2-graphene heterojunction devices. Experimental results on the heterojunction device indicate a high concentration of unintentional donors in natural MoS2 to be 3.57 x 1011 cm[-]2, while the ionized donor concentration is determined to be 3.61 x 1010 cm[-]2, which implies the presence of deep donors. The high donor concentration and the resulting high electric field near the heterojunction interface suggest that the charge transport mechanism is thermionic-field emission in a low bias region. Based on this model, the barrier height of the graphene-MoS2 heterojunction is determined to be 0.23 eV. The second theme of the thesis is optical characteristics of the heterojunction devices. The results from scanning photocurrent microscopy measurements with multiple bias conditions indicate a photothermal electric (PTE) effect is the dominant mechanism for photoresponse in a graphene-MoS2 heterojunction. The photothermal voltage generated by the PTE effect is estimated to be 0.22[-]0.47 mV and induces the photocurrent. Photoresponses of 0.139 mA/W and 0.019 mA/W on the graphene- MoS2 heterojunction area are observed with and without a bias of 0.3 V, respectively, using an 800 nm wavelength laser at 0.43 mW power.