The TROPOspheric Monitoring Instrument (TROPOMI) level-2 aerosol layer height (ALH) product has now been released to the general public. This product is retrieved using TROPOMI's measurements of the oxygen A-band, radiative transfer model (RTM) calculations augmented by neural networks and an iterative optimal estimation technique. The TROPOMI ALH product will deliver ALH estimates over cloud-free scenes over the ocean and land that contain aerosols above a certain threshold of the measured UV aerosol index (UVAI) in the ultraviolet region. This paper provides background for the ALH product and explores its quality by comparing ALH estimates to similar quantities derived from spaceborne lidars observing the same scene. The spaceborne lidar chosen for this study is the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) mission, which flies in formation with NASA's A-train constellation since 2006 and is a proven source of data for studying ALHs. The influence of the surface and clouds is discussed, and the aspects of the TROPOMI ALH algorithm that will require future development efforts are highlighted. A case-by-case analysis of the data from the four selected cases (mostly around the Saharan region with approximately 800 co-located TROPOMI pixels and CALIOP profiles in June and December 2018) shows that ALHs retrieved from TROPOMI using the operational Sentinel-5 Precursor Level-2 ALH algorithm is lower than CALIOP aerosol extinction heights by approximately 0.5km. Looking at data beyond these cases, it is clear that there is a significant difference when it comes to retrievals over land, where these differences can easily go over 1km on average.