The efficient development of carbonate rock reservoirs with rich oil and gas resources has become a hot topic and a focal point in the current oil and gas industry. The development of carbonate rock oil and gas reservoirs differs from that of sandstone reservoirs. Although gas flooding, water flooding, and chemical flooding have been carried out in recent years, the development is still unsatisfactory, and the on-site application of technologies such as nanoparticles is on the rise. For the future development of acid fracturing technology, accurate reservoir geological description, core printing based on additive manufacturing technology, the development of new acid fracturing techniques, and the research and development of acid fracturing equipment will have great research potential and economic value in the development of carbonate rock oil and gas reservoirs. Under the development background of high-temperature deep reservoirs, this paper comprehensively reviews unconventional acidizing fracturing fluids in carbonate rock oil and gas reservoirs. We introduce the main components, corresponding mechanisms of action, current research achievements, and advantages of promising acid fracturing fluids, including thickened acids. We focus on the application and limitations under harsh conditions of high temperature and high salinity while also focusing on the development of thickened acid fracturing technology. The thickening agent is the core of a thickened acid solution. Therefore, this article fully reviews the structure, sources, advantages and disadvantages, as well as the current development status of biological, cellulose, and synthetic polymer thickeners. Synthetic polymers, low-molecular-weight polymers, and small-molecular compound crosslinkers provide clues for temperature and salt-resistant thickeners and also promote the development of tight reservoirs.