Limestone is one of the most common kinds of sedimentary rock - about a tenth of all sedimentary rock is limestone. It's just as well that it's common, because it's incredibly useful not just as a building material in its unprocessed form, but also as the main raw ingredient of cement (hence also concrete) and quicklime, which among other things is a standard ingredient in glass production. It's also crushed up and used as a foundation to build roads on, ground up finely to add to toothpaste or excessively acidic soil, and used in a wide range of other industrial processes. Britain alone digs up 76 million tonnes of limestone every year1 - that's more than a tonne for every person on the island!
Limestone is also known for its fossils - something it has in common with some other sedimentary rocks, notably shale. Many of the best-preserved fossils found have been discovered in limestone, and in fact limestone itself is largely composed of the fossilised remains of coral and other marine invertebrates. Limestone is susceptible to erosion by acid and to a lesser extent plain old water. This is usually a very slow process, though - most cave systems have been carved out of limestone bedrock by rainwater over the course of millions of years, but the Great Pyramid of Giza is still in pretty good shape. However, acid rain accelerates the process hugely, and conserving buildings and monuments made of limestone has become a much bigger concern since the rise of mass industry.
Limestone often contains some silica, but it is mainly composed of calcium carbonate (CaCO3), as are chalk, marble (which is limestone that has been transformed by extreme heat and pressure) and limescale (which is largely limestone that has been dissolved in the water supply and then deposited on the inside of your kettle). That is why limestone is so vulnerable to acid, including the carbonic acid you get when carbon dioxide (CO2) dissolves in water - the calcium carbonate reacts quite strongly with many acids, turning into chemicals which then dissolve readily. That in turn is one reason why the rising concentration of CO2 in our atmosphere is a cause for concern: as the oceans absorb CO2, they become more acidic, making it impossible for many marine organisms to form the shells and skeletons they rely on.
Those same shells and skeletons would eventually become limestone if they got the chance, and part of the reason they won't is that the processing of limestone into cement contributes enormously to the rise in global CO2. It takes high temperatures to bring about the necessary chemical reactions, which also release CO2 from the rock. It has been estimated that between 2%2 and 5%3 of global carbon emissions or more come from the manufacture of cement, and that figure is still rising. There are several possible ways of reducing these emissions4, many of them already widely adopted in rich countries but less so in developing countries where cement production is growing rapidly. None of them are used universally, and development of some of the more radical possibilities for emissions reduction has been slow. After all, the costs of emitting CO2 are almost always borne by someone else.
The chemistry of cement production is quite straightforward, and in its basics it was known to the ancient Romans and others. Limestone or another source of calcium carbonate is heated to around 800°C, causing it to glow brightly and decompose into CO2 and calcium oxide, also known as quicklime. This is a powerful alkali, with many uses. Portland cement is made from a mix of this and powdered clay; add in sand and pebbles, and you have concrete. The ancient Romans used volcanic ash rather than clay, which may have something to do with why the Colosseum has stood up so well5. When quicklime is mixed with water, it reacts to form calcium hydroxide (slaked lime - see also 'a small green vial in a Bengali supermarket'), letting off a great deal of heat in the process. Civilisations in many parts of the world used slaked lime cement as a building material, as much as 5000 years ago - often holding together blocks of limestone.
1 Edexcel GCSE Science
2 National Cement Production Estimates: 1950 - 2010
3 Carbon Dioxide Emissions from the Global Cement Industry
4 Decoupling carbon emissions from cement production
5 The Secrets of Ancient Rome’s Buildings