Extensive surveys of galaxy clusters motivate us to assess the likelihood of cluster–cluster lensing (CCL), namely, gravitational lensing of a background cluster by a foreground cluster. We briefly describe the characteristics of CCLs in optical, X-ray and Sunyaev–Zel'dovich effect measurements, and calculate their predicted numbers for Λ cold dark matter (ΛCDM) parameters and a viable range of cluster mass functions and their uncertainties. The predicted number of CCLs in the strong-lensing regime varies from several (<10) to as high as a few dozen, depending mainly on whether lensing triaxiality bias is accounted for, through the c–M relation. A much larger number is predicted when taking into account also CCL in the weak-lensing regime. In addition to few previously suggested CCLs, we report a detection of a possible CCL in A383, where background candidate high-z structures are magnified, as seen in deep Subaru observations.