Space borne millimeter radar (CloudSat CPR) data have been used to identify and analyze both bulk and internal structures of MCS anvil clouds. As detected by CloudSat CPR, tropical MCSs are found to be dominated by cloud-top heights >10 km. Secondary cloud layers sometimes occur in MCSs, but outside their primary raining cores. The secondary layers have tops at 6-8 and 1-3 km. High-topped clouds extend outward from raining cores of MCSs to form anvil clouds. The modal thickness of MCS anvils is 45 km. Anvils are mostly confined to within 1.52 times the equivalent radii of the primary rain areas of the MCSs. The warm ocean MCSs tend to have the thickest (i.e. > ~10km in depth) non-raining and lightly raining anvils near the edges of their actively raining regions, indicating that anvils are generated in and spread out from the primary raining regions of the MCSs. Such thick anvils are nearly absent over continental regions. Closest to the raining cores, the anvils tend to have broader distributions of reflectivity at all levels, with the modal values at higher reflectivity in their lower levels. Portions of anvil clouds far away from the raining core are thin and have narrow frequency distributions of reflectivity at all levels with overall weaker values. This difference likely reflects ice particle fallout and therefore cloud age. Reflectivity histograms of MCS anvil clouds vary little across the tropics except: i) in continental MCS anvils, broader distributions of reflectivity occur at the uppermost levels in the portions closest to active raining areas; ii) the frequency of occurrence of stronger reflectivity in the upper part of anvils decreases faster with increasing distance in continental MCSs; iii) narrower-peaked ridges are prominent in reflectivity histograms of thick anvil clouds close to the raining areas of connected MCSs (superclusters). These global results are consistent with observations at ground sites and aircraft data. They present a comprehensive test dataset for models aiming to simulate process-based upper-level cloud structure around the tropics.