In recent years, soft robotics has developed considerably, especially since the year 2018 when it became a hot field among current research topics. The attention that this field receives from researchers and the public is marked by the substantial increase in both the quantity and the quality of scientific publications. In this review, in order to create a relevant and comprehensive picture of this field both quantitatively and qualitatively, the paper approaches two directions. The first direction is centered on a bibliometric analysis focused on the period 2008-2022 with the exact expression that best characterizes this field, which is "Soft Robotics", and the data were taken from a series of multidisciplinary databases and a specialized journal. The second direction focuses on the analysis of bibliographic references that were rigorously selected following a clear methodology based on a series of inclusion and exclusion criteria. After the selection of bibliographic sources, 111 papers were part of the final analysis, which have been analyzed in detail considering three different perspectives: one related to the design principle (biologically inspired soft robotics), one related to functionality (closed/open-loop control), and one from a biomedical applications perspective.