In ΛCDM, the abundance and “height” of density peaks that collapse into halos and clusters is predicted by Gaussian initial conditions and calibrated by the linear power spectrum and growth history, leading to specific expectations for the high-mass end of the halo mass function and the statistics of rare peaks (Press & Schechter 1974; Sheth & Tormen 1999). Observations and simulations, however, sometimes reveal either an excess or deficit of very massive clusters and extreme peaks compared to these baseline predictions, as well as environment-dependent peak statistics, hinting that the simple Gaussian peak theory plus standard growth in ΛCDM may not fully capture how rare, high-s peaks form in the real universe (Jenkins et al. 2001; Bhattacharya et al. 2011).