Past theories of acids and bases tend to purely rely on what was believed to be the chemical composition of all acids and their properties. Lavoisier's theory stated that acids were substances which contained hydrogen, as he found that when compounds involving oxygen dissolved in water, they produced acidic properties, such as CO2, NO2 and P4O10. This also meant that some acids were recognised to be acids, e.g. H2SO4. However, this is now known to be significantly flawed, as some substances containing oxygen are in fact basic (e.g. Na2CO3, Na2O) and why some other acids did not contain oxygen (e.g. HCl). Davy then proposed that acids were substances that contained hydrogen through the discovery of HCl, through means of dissolving gaseous hydrogen chloride into water and producing a highly acidic solution. Davy also found that metals could displace the hydrogen in acids: Metal + Acid -> Salt + Hydrogen gas. Yet, this was also flawed because other substances such as CH4 are not acidic, yet also contain hydrogen.
Arrhenius then developed a theory that was, at the time, much more revolutionary and a more accurate definition of acids, and bases. Arrhenius showed that acids were substances that when dissolved in water, ionised to form H+ ions, and similarly for bases albeit OH- ions. Arrhenius was also able to initiate the definitions of relative strengths of acids through his theory from an understanding of degrees of ionisation, and also demonstrated how acids and bases can undergo a neutralisation process: Acid + Base -> Salt + Water. This is reasonably accurate, and is sometimes taught as a simplified model of how acids and bases work, however it did not cater for other bases such a Na2CO3 and NH3.
The most accurate definition of acids and bases was proposed by Johannes Bronsted and Thomas Lowry. The Bronsted-Lowry theory defines acids and bases in terms of their chemical behaviour, that is, acids were substances that could donate a proton/protons, whereas bases could accept them. This theory focused much more on the properties of acids and bases rather than their chemical composition and an understanding of what conjugate acids and bases were. By consideration of the ability to donate/accept H+, it was then finally understood why substances were acidic, basic or neutral. (It also led into the identification of amphiprotic species with reference conjugate acids and bases.)