Probing the magnetic nature of the Sun's chromosphere requires measurement of the polarization profiles of relevant magnetically sensitive spectral lines, many of which are in the ultraviolet spectrum, necessitating observations above the absorbing terrestrial atmosphere. The CLASP series of sounding rocket missions were designed to develop and test a technique for observing the Sun in ultraviolet light, and for quantifying the polarization of that light. By demonstrating successful measurement and interpretation of the polarization in hydrogen Lyman-α and the Mg II h and k spectral lines, these missions are crucial steps towards routine quantitative characterization of the local thermal and magnetic conditions in the solar chromosphere. In the most recent observations, CLASP2.1, the spectrograph slit was scanned across an active region plage to acquire a two-dimensional map of Stokes V/I, to demonstrate the ability of UV spectropolarimetry to yield chromospheric magnetic fields over a large area. The technique yields a set of simultaneous line-of-sight magnetograms at multiple heights within the plage atmosphere. By combining the CLASP2.1 measurements with magnetograms from Hinode/SOT or SDO/HMI, a wide range of atmospheric heights are mapped, from the photosphere to the upper chromosphere.