The demand for alternative and renewable energy has been increasing globally over the years as the world faces fuel shortage crisis. To solve this crucial challenge to the society, thermoelectric materials have received growing attention as they can generate electricity from waste heat and conversely create a temperature difference when voltage gradient is applied. The thermoelectric power generation, cooling and heating applications are based on solid-state devices with no moving parts which leave the material characteristics as the measurement of the efficiency, which is the dimensionless thermoelectric figure of merit, ZT = S2σT/κ, where S, σ, T and κ are the Seebeck coefficient, electrical conductivity, absolute temperature and thermal conductivity, respectively. The difficulty of optimization of ZT lies in the fact the above parameters are generally interdependent. For example, σ is proportional to n/m*, where n and m* are the carrier concentration and effective mass respectively, while S is proportional to m*/n2/3and κ is proportional to σ; hence traditional materials with larger σ normally have smaller S and larger κ. Therefore, it is a challenge to develop advanced thermoelectric materials with optimization of these conflicting properties to increase ZT.One way to increase ZT is using low-dimensional materials systems, such as quantum wells, quantum wires and quantum dots. [1] All these structures lead the thermoelectric ZT to be significantly improved because of the quantum confinement effects to enhance power factor S2σ, and concurrently remain the thermal conductivity low. For an example, experiments have been conducted by two groups of researchers that prove silicon nanowires are efficient thermoelectric materials due to the suppression of phonon conductivity by surface roughness. [2,3] Among these many materials studied, two-dimensional material, such as graphene related materials, MoS2, etc., have been extensively studied and generated considerable interesting due to their unique electronic, optoelectronic, and phononic properties. For example, cutting the different edge and shape of graphene to form various nanoribbons can significantly change their electron and phonon transport behaviors indicating the capability of controlling the thermoelectric performance. [4] In this work, therefore, I shall firstly give the introduction to fundamental understanding of electron and phonon transport in the nanoscale materials using quantum transport and ballistic transport theories. Next, I will discuss the fundamentals of material properties of these advanced 2D materials including graphene and beyond graphene, such as transition metal dichalcogenides (TMDs) with single layered and multiple layered structures. Interestingly, the results show that two layered WSe2 has the best ZT compared to the different layered WSe2 and MoS2due to its unique electronic bandstructure. [5,6] However, for practical applications, defect and structure engineering may be needed to improve ZT significantly. [4,7]AcknowledgementI will like to thank my collaborators, Wen Huang, Xin Luo, Chee Kwan Gan, Su Ying Quek, Xiaoxi Ni, Baowen Li, and Jian-Sheng Wang, for their contributions in this work.Reference[1] G. Chen, M. S. Dresselhaus, G. Dresselhaus, J. P. Fleurial, and T. Caillat, Int. Mater. Rev. 48, 45 (2003).[2] A. I. Boukai, Y. Bunimovich, J. T. Kheli, J. K. Yu, W. A. Goddard, and J. R. Heath, Nature 451, 168 (2008).[3] A. I. Hochbaum, R. K. Chen, R. D. Delgado, W. J. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. D. Yang, Nature 451, 163 (2008).[4] W. Huang, J. Wang, and G. Liang, “Phys. Rev. B 84, 045410 (2011).[5] W. Huang, H. Da, and G. Liang, Journal of Applied Physics 113, 104304, (2013).[6] W. Huang, X. Luo, C. Gan, S. Quek, and G. Liang, submitted for publsication.[7] X. Ni, G. Liang, J. Wang, and B. Li, Appl. Phys. Lett. 95, 192114, (2009).