Light detection and ranging (LiDAR) remote sensing systems are deployed in various platforms including satellites, airplanes, and drones—which, in essence, determines the sampling characteristics of the underlying imaging system. Low-altitude LiDARs provide high photon count and high spatial resolution but only in very localized patches. Satellite LiDARs, on the other hand, provide measurements at a global scale but are limited by low photon count and their samples are sparsely apart along swath line trajectories that are far in between. This article describes a new class of satellite remote sensing LiDARs, aimed at overcoming the limitations of current satellite imaging systems. It exploits the principles of compressive sensing and machine learning (ML) to compressively sense Earth from hundreds of kilometers above Earth to then reconstruct the 3-D imagery with resolution and coverage, as if the data were collected from airborne platforms at just hundreds of meters in height. We introduce a novel representation of waveform altimetry profiles, coined hyperheight data cubes (HHDCs), which encompass rich information about the 3-D structure of a scene. Canopy height models (CHMs), digital terrain models (DTMs), and many other features of a scene that are embedded in HHDC are easily extracted with simple statistical quantiles. We introduce ML methods to reconstruct the compressive LiDAR measurements so as to attain high-resolution, dense coverage, and broad field-of-view per swath pass. ML training data are attained from NASA’s G-LiHT imaging missions. Simulations with various types of forests across the US illustrate the power of the new LiDAR imaging systems.