The effects of metallic contacts on electronic transport of graphene had not been completely estimated however widely discussed [1-3], hence we propose two powerful methods, i.e., exact [4] and renormalized transfer matrix method [5,6].On one hand, results from exact transfer-matrix methods are valid for all sheet widths and lengths.In the limit of the large width-to-length ratio relevant to recent experiments, we find a Dirac-point conductivity of 2e2/√/3h and a sub-Poissonian Fano factor of 2-3√3/π=0.346 for armchair graphene;for the zigzag geometry they are respectively 0 and 14.On the other hand, renormalized transfer matrix method (RTMM) [5] utilizes U times of multiplication of traditional transfer matrix (U linear to the length) to eliminate numerical instability.Then optimized Gauss elimination greatly reduces the computational complexity from O(U3) to O(U).RTMM is powerful to investigate transport in large scale system (up to 106 carbon atoms) with irregular structure, disorder and impurity, and under magnetic field.Stress leads to deformation of graphene and spontaneously affects change of hopping integrals.Consistent with observations, the conductance through graphene nanoribbons (GNRs) monotonically decreases, when the stress is parallel to the transverse direction [7].As the stress is perpendicular to the transverse direction, the conductance increases till the gap opens in armchair GNRs (AGNRs), while monotonically increases in ZGNRs.Transport through neutral and strained AGNRs is completely determined by the edge state of strained ZGNRs.Conductance through strained ZGNRs between quantum wire contacts is linear with the width and one quantized conductance as t2, i.e., hopping integral perpendicular to the transverse direction, equals to 0 and 1 respectively.We reveal essential effects from both the topology of graphene and the leads [4,6,7], giving a complete microscopic understanding of the unique transport in graphene.