The variation between land surface temperature (LST) within a city and its surrounding area is a result of variations in surface cover, thermal capacity and three-dimensional geometry. The objective of this research is to review the state of knowledge and current research to quantify surface urban heat islands (SUHI) and surface urban cool islands (SUCI). In order to identify open issues and gaps remaining in this field, we review research on SUHI/SUCI, the models for simulating UHIs/UCIs and techniques used in this field were appraised. The appraisal has revealed some great progress made in surface UHI mapping of cities located in humid and vegetated (temperate) regions, whilst few studies have investigated the spatiotemporal variation of surface SUHI/SUCI and the effect of land use/land cover (LULC) change on LST in arid and semi-arid climates. While some progress has been made, models for simulating UHI/UCI have been advancing only slowly. We conclude and suggest that SUHI/SUCI in arid and semi-arid areas requires more in-depth study.