Multicore fiber (MCF) which contains more than one core in a single fiber cladding has attracted ever increasing attention for application in optical sensing systems owing to its unique capability of independent light transmission in multiple spatial channels. Different from the situation in standard single mode fiber (SMF), the fiber bending gives rise to tangential strain in off-center cores, and this unique feature has been employed for directional bending and shape sensing, where strain measurement is achieved by using either fiber Bragg gratings (FBGs), optical frequency-domain reflectometry (OFDR) or Brillouin distributed sensing technique. On the other hand, the parallel spatial cores enable space-division multiplexed (SDM) system configuration that allows for the multiplexing of multiple distributed sensing techniques. As a result, multi-parameter sensing or performance enhanced sensing can be achieved by using MCF. In this paper, we review the research progress in MCF based distributed fiber sensors. Brief introductions of MCF and the multiplexing/de-multiplexing methods are presented. The bending sensitivity of off-center cores is analyzed. Curvature and shape sensing, as well as various SDM distributed sensing using MCF are summarized, and the working principles of diverse MCF sensors are discussed. Finally, we present the challenges and prospects of MCF for distributed sensing applications.