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The entry Acidity and Basicity explains what acids and bases are. In essence, acids and bases are a way of classifying substances according to a very special form of reaction, namely the exchange of protons ebetween chemical compounds. For more information please consult that entry. The historic evolution of the concepts 'acid' and 'base' is another topic altogether. That's what this entry is about.
In a first attempt to characterise substances, the concepts of acids and bases were loosely defined as substances that change some properties of water. Much later (in the 19th Century) the composition of acids and bases was elucidated, bringing a very narrow definition of acids and bases. These concepts evolved even further to become broader again, yet still very fuzzily defined. These concepts are a very useful tool in chemical reasoning. Nowadays, virtually anything can be seen as an acid or a base.
In the Beginning
The starting point for most of the scientific historical evolutions is, as usual, the Mediterranean region in BC-times, Greece in particular. There, some smart people were trying to unravel nature's secrets. One first step in that direction was to sort all kinds of substances in an attempt to characterise nature.
One of the criteria used, which everyone thought was good, was the taste of stuff. According to this criterion the first categories were: salty-tasting stuff, sour-tasting stuff, sweet-tasting stuff, and bitter-tasting stuff. Sour-tasting stuff would give rise to the word 'acid', which comes from the Greek word oxein, which mutated into the Latin verb acere, which means 'to make sour'(thus the term 'acetic acid', which is the sour tasting component in vinegar, is a redundancy).
With the passing of time, people found out that the sour-tasting stuff had some other properties in common, apart from just tasting sour; for example, it changes the colour of litmus1 and corrodes some metals. It is for this reason that the classification term 'acid' is the only category originally based on taste still in use today. The reasons for the taste of the other stuff were found to be of a more complicated nature, which is the reason why the rest of the categories are no longer in use.
It was not until modern times, that the fundamental working mechanisms and the chemistry of acids was elucidated. One first attempt was delivered by a famous French man named Antoine Laurent Lavoisier (1743-1796). He used to perform chemistry shows for the wealthy noblesse in Paris, making a good extra buck in that way.
Lavoisier was a remarkable and well-funded scientist, the so-called father of modern chemistry, who eventually lost his head to the French Revolution. Before he did that, however, he was one of the first people to try out a chemical classification of substances. By 1776, he had come up with the idea that a certain compound, element, or essence in the acid would be responsible for its acidity. For that reason he called the substance oxy-gene2, or 'oxygen' as we know it today. Eventually, this idea turned out to be wrong. Nevertheless, it was a good beginning.
The British scientist Humphry Davy (1778-1829), who among other things discovered the medicinal uses of nitrous oxide (laughing-gas) by self-experimentations, continued these investigations; and by 1810, he found out that the oxygen was not responsible for the acidity, since certain acids would be acid without containing any oxygen.
In Munich, by the 1840s, Justus Freiherr von Liebig (1803-1873), one of the big chemistry hot-shots in Germany and the founder of agro-chemistry, proposed that the acidity was generated by hydrogen, because it is the component all acids have in common. Now this idea was a very good one, as one will see later... Before starting on that, let us not forget the bases.
Bases were identified and categorised as the substances which are neutralising acids. For that reason, the progress in the characterisation of bases was always connected to the more popular characterisation of acids. As a consequence, the theories for bases were always overshadowed by the theories for acids. Nevertheless, bases have also been known for a long time.
The associated word 'alkaline' (which is used to describe the properties of a base-solution, like its soapy taste) has Arabic roots. The term originally meant 'roasting', because the first alkaline substances were obtained by roasting ashes then treating them with water and slaked lime (calcium hydroxide). The substances obtained are sodium and potassium hydroxide, two of the most classic bases, which were used to make soap.
The use of the word 'base' to describe these substances was introduced a lot later; the original rationale remains obscure. One possibility is that the 'bases' were the basic (in the sense of 'fundamental') compounds used to form salts with acids. Another possibility is that it's called that just to add confusion. The second theory has many adherents among chemistry students.
Conventional Acid-Base Theory after 1850
Based on the research made by Davy, Liebig, and others, a more precise definition of acids (and bases) followed in 1894.
In the middle of this development was the Swedish chemist, Svante August Arrhenius (1859-1927), a misunderstood genius who was way ahead of his time. He had the insolence to propose in his doctoral thesis that certain substances remain ionised in solution. In 1884, this constituted an act of scientific heresy. Of course, everybody thought Arrhenius was a weirdo. He was scornfully awarded a fourth class degree, and was obviously left feeling very hurt. Years later, in 1903, he was proven right: he got his revenge and the Nobel Prize.
According to Arrhenius, the definition of acids and bases went like this:
Acids are substances delivering hydrogen cations (positively charged hydrogen, often simply called proton or abbreviated H+) to the solution (water).
HCl and H2SO4 (cf. footnote3) which form H+ and Cl- or SO42-, respectively, dissolved in water.
Bases are substances delivering hydroxyl anions (OH-) to the solution (water).
NaOH and Ca(OH)2 (cf. footnote4) which form OH- Na+ and Ca2+, respectively, dissolved in water.
Acids and bases react in a neutralisation reaction to form water (where H+ reacts with OH- to form H2O) and the corresponding salt (In the examples: NaCl, Na2SO4, CaCl2 or CaSO4).
Brønsted and Lowry
Inspired by the work of Arrhenius, a Danish fellow named Johannes Nicolaus Brønsted and, independently, an Englishman by the name of Thomas Martin Lowry extended the acid-base theory to what is nowadays being taught in school, the Brønsted-Lowry concept. Here are the definitions according to those august gentlemen:
Acids are substances from which a proton (H+) can be removed.
Bases are substances that bind protons.
These definitions mutated somewhat to become the slightly less accurate school-book-definition, in which acids are proton 'donors' and bases proton 'acceptors'. The notion of a substance 'donating' protons is wrong: no one and nothing in this world - not even molecules or elements - will donate anything for free. One will always need energy to break the bond. The acid and base strength is defined by the strength with which the proton is bound to the base.
According to this theory any compound capable of binding a proton is a base5. So, all components can be seen as bases, since virtually anything can bind protons. The question is, what binds the proton more strongly? Being a base or an acid will depend on what you are comparing it to. If the referring system is water (as it usually is), then anything binding protons stronger than water is a base and anything binding protons weaker than water will be an acid. This is roughly how acids and bases are categorised. A more detailed description, with some maths can be found in the Edited Entry, Acidity and Basicity.
Modern Acid-Base Theory
Gilbert Newton Lewis
For a long time the referring system was water. Stuff giving protons (protonating) to water is acid; stuff water protonates is a base. An extension to that theory was brewed up by the American chemist, Gilbert Newton Lewis (1875-1946), where the 'donation' is no longer tied to water. The 'donation' is in fact not even restricted to protons. According to Lewis, the crucial things being 'donated' and 'removed' are charges.
Positive charges are acid and negative charges are bases. This does not change the whole Brønsted concept, but widens the acid-base concept immensely. Now you can dissolve zinc dichloride (ZnCl2) in pentachloropyridine (Cl5C5N) and say that the zinc compound is the acid and that the pentachloropyridine is the base - the formulas and the names can perfectly well be ignored, just take note of the fact that there is no proton or oxygen involved in this acid-base reaction.
Magic Acids and Super-Bases
During the 1930s, people tried to synthesise ever stronger acids. Pure sulphuric acid with an additional substance called fluorosulphuric acid was millions of times more acidic than anything ever observed. People went nuts about it! Those acids were called 'superacids'.
A further leap in acidity came in the 1970s, when additional antimonypentafluoride was added to the 'superacid'. These acids are millions of times stronger than the superacids. The scientific community was speechless. These mixtures are so acid that they do not only lose their protons to anything, they even force stuff to accept them. For instance methane is forced to bind the proton. This substance is then so unstable that it will form hydrogen and ethane.
For those who are not experienced in chemistry, it's enough to say that this reaction is incredible. The term 'magic acid' was coined by George A Olah, who synthesised these acids and got his Nobel chip in 1994. Magic acids are thousands of trillions times stronger than 1M H2SO4.
The counterpart of super-acids are super-bases - alkali-organyls, like butyl-potassium, for example. These compounds will rip off hydrogen cations from virtually anything. Super-bases had not been 'invented' in the same sense the 'super acids' were, partly because it's easier to rip protons off substances than forcing them to bind it. The term 'super-base' is of modern origin, but super-bases have been used since the 1850s.