Surface plasmon polaritons (SPPs) have found many important applications in on-chip signal transportation, enhanced nonlinear/Raman effect, biological/chemical sensing, super resolution imaging, etc. In these applications, the near-field propagation and far-field scattering of SPPs play a vital role. However, there has been strong desire to understand these physical effects. In this paper, we first briefly review the history and progress of SPPs. Next, we mainly focus on the near-field propagation and far-field scattering of SPPs, including their fundamental theories and practical applications. Finally, we review several different approaches to manipulating the near-field wavefronts of SPPs. These researches offer us a more in-depth understanding and the ability to more strongly control the scattering characteristics of SPPs, which may promote the scientific researches and practical applications of SPPs in the future.