  Recent advances in the development of Josephson scanning tunneling
spectroscopy (JSTS) have opened a new path for the exploration of
unconventional superconductors. We demonstrate that the critical current,
$I_c$, measured via JSTS, images the spatial form of the superconducting order
parameter in $d_{x^2-y^2}$-wave superconductors around defects and in the
Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that $I_c$ probes the
existence of phase-incoherent superconducting correlations in the pseudo-gap
region of the cuprate superconductors, thus providing unprecedented insight
into its elusive nature. These results provide the missing theoretical link
between the experimentally measured $I_c$, and the spatial structure of the
superconducting order parameter.
