Deflecting and crabbing structures have many applications in current accelerator systems. The primary use of a deflecting cavity is to separate a single beam into multiple beams. A crabbing cavity enables the head-on collision at the interaction point in particle colliders in order to increase the luminosity. The early uses of the deflecting structures have been in the early 1960s: these structures were disk loaded structures operating at room temperature. The crabbing structure which was installed at the NEK electron-positron collider was the first and only operational superconducting cavity of that kind. The most common design of superconducting deflecting and crabbing cavities is a squashed-elliptical geometry operating in a TM110-like mode: at low frequencies these structures become challenging due to the large geometrical shapes. Recently, compact deflecting and crabbing structures have been studied for numerous accelerator applications not limited to deflecting or crabbing of beams. but also for beam diagnostics, emittance exchange etc. The rf-dipole design, which is presented here, has evolved from the parallel-bar design and is a new compact deflecting and crabbing design with attractive properties at low frequencies and is operating in a TE11-like mode. The parallel-bar design has been optimized into the rf-dipole design primarily to maximize the net deflection with low and balanced peak surface fields and also to maximize the shunt impedance. The geometries have also been modified to increase the separation between the higher order modes, suppress multipacting conditions and reduce multipole components. The design geometries have been improved for mechanical stability in order to withstand thermal and pressure fluctuations under operating conditions. Two superconducting rf-dipole deflecting and crabbing cavities have been designed and optimized at 499 MHz for the Jefferson Lab 12 GeV Upgrade and at 400 MHz for a crabbing cavity for the LHC Luminosity Upgrade. The design optimization, fabrication, and test results of the first prototypes of both designs are presented in detail