In ΛCDM, the abundance and heights of peaks in the smoothed matter or weak-lensing convergence field are predicted from an almost-Gaussian initial density field evolved under gravity, so peak counts at given signal-to-noise should match halo-model and simulation-based expectations once survey noise and projection effects are included (Bardeen et al. 1986; Coles 2002). Yet several analyses of peak statistics in galaxy and shear maps report either fewer high peaks or a different distribution of peak heights than standard ΛCDM models tuned to CMB and cluster counts, hinting at missing physics, nontrivial baryonic or line-of-sight effects, or a breakdown of the simplest halo-based description on the relevant scales (Peacock & Dodds 1996; Hoekstra 2001).