We discuss propagation behaviors of surface plasmons (SPs) in 2-dimensional (2D) and 1-dimensional (1D) materials, such as graphene and carbon nanotubes. Firstly, we introduce recent theoretical and experimental studies on the reflections of SPs at the edge of 2D material, and discuss corresponding anomalous phase shifts. Also, we extend our theoretical model to describe the tunneling of SPs through an abrupt nano-gap in 2D surface. Specifically, we examine gap-size dependent tunneling efficiency and the nature of phase shift. Finally, we apply our model to explain SP interaction with the end of 1D material, and discuss how the SP reflection in the 1D system can be described.