There are altogether seven remaining complete capitals, five with lions, one with an elephant and one with a zebu bull.
One of them, the four lions of Sarnath, has become the State Emblem of India.
The animal capitals are composed of a lotiform base, with an abacus decorated with floral, symbolic or animal designs, topped by the realistic depiction of an animal, thought to each represent a traditional directions in India.

Various foreign influences have been described in the design of these capitals.
 The animal on top of a lotiform capital reminds of Achaemenid column shapes.
The abacus also often seems to display some influence of Greek art: in the case of the Rampurva bull or the Sankassa elephant, it is composed of honeysuckles alternated with stylized palmettes and small rosettes.
 A similar kind of design can be seen in the frieze of the lost capital of the Allahabad pillar.
These designs likely originated in Greek and Near-Eastern arts.
They would probably have come from the neighboring Seleucid Empire, and specifically from a Hellenistic city such as Ai-Khanoum, located at the doorstep of India.
Most of these designs and motifs can also be seen in the Pataliputra capital.

The Diamond throne of Bodh Gaya is another example of Ashokan architecture circa 260 BCE, and displays a band of carvings with palmettes and geese, similar to those found on several of the Pillars of Ashoka.

Chronological order
Based on stylistic and technical analysis, it is possible to establish a tentative chronological orders for the pillars.
The earliest one seems to be the Vaishali pillar, with its stout and short column, the rigid lion and the undecorated square abacus.
Next would follow the Sankissa elephant and the Rampurva bull, also not yet benefiting from Mauryan polish, and using a Hellenistic abacus of lotus and palmettes for decoration.
The abacus would then adopt the Hamsa goose as an animal decorative symbol, in Lauria Nandangarh and the Rampurva lion.
Sanchi and Sarnath would mark the culmination with four animals back-to-back instead of just one, and a new and sophisticated animal and symbolic abacus (the elephant, the bull, the lion, the horse alternating with the Dharma wheel) for the Sarnath lion.

Other chronological orders have also been proposed, for example based on the style of the Ashokan inscriptions on the pillars, since the stylistically most sophisticated pillars actually have the engravings of the Edicts of Ashoka of the worst quality (namely, very poorly engraved Schism Edicts on the Sanchi and Sarnath pillars, their only inscriptions).
This approach offers an almost reverse chronological order to the preceding one.
According to Irwin, the Sankissa elephant and Rampurva bull pillars with their Hellenistic abacus are pre-Ashokan.
Ashoka would then have commissioned the Sarnath pillar with its famous Lion Capital of Ashoka to be built under the tutelage of craftsmen from the former Achaemenid Empire, trained in Perso-Hellenistic statuary, whereas the Brahmi engraving on the very same pillar (and on pillars of the same period such as Sanchi and Kosambi-Allahabad) was made by inexperienced Indian engravers at a time when stone engraving was still new in India.
After Ashoka sent back the foreign artists, style degraded over a short period of time, down to the time when the Major Pillar Edicts were engraved at the end of Ashoka's reign, which now displayed very good inscriptional craftsmanship but a much more solemn and less elegant style for the associated lion capitals, as for the Lauria Nandangarh lion and the Rampurva lion.

Of the Allahabad pillar, only the abacus remains, the bottom bulb and the crowning animal having been lost.
The remains are now located in the Allahabad Museum.

A few more possibly Ashokan capitals were also found without their pillars:
Kesariya (capital).
Only the capital was found in the Kesaria stupa.
It was discovered by Markham Kittoe in 1862, and said to be similar to the lion of the Lauriya Nandangarh pillar, except for the hind legs of the lion, which did not protrude beyond the abacus.
There are altogether seven remaining complete capitals, five with lions, one with an elephant and one with a zebu bull. One of them, the four lions of Sarnath, has become the State Emblem of India. The animal capitals are composed of a lotiform base, with an abacus decorated with floral, symbolic or animal designs, topped by the realistic depiction of an animal, thought to each represent a traditional directions in India.
Various foreign influences have been described in the design of these capitals.  The animal on top of a lotiform capital reminds of Achaemenid column shapes. The abacus also often seems to display some influence of Greek art: in the case of the Rampurva bull or the Sankassa elephant, it is composed of honeysuckles alternated with stylized palmettes and small rosettes.  A similar kind of design can be seen in the frieze of the lost capital of the Allahabad pillar. These designs likely originated in Greek and Near-Eastern arts. They would probably have come from the neighboring Seleucid Empire, and specifically from a Hellenistic city such as Ai-Khanoum, located at the doorstep of India. Most of these designs and motifs can also be seen in the Pataliputra capital.
The Diamond throne of Bodh Gaya is another example of Ashokan architecture circa 260 BCE, and displays a band of carvings with palmettes and geese, similar to those found on several of the Pillars of Ashoka.
Chronological order
Based on stylistic and technical analysis, it is possible to establish a tentative chronological orders for the pillars. The earliest one seems to be the Vaishali pillar, with its stout and short column, the rigid lion and the undecorated square abacus. Next would follow the Sankissa elephant and the Rampurva bull, also not yet benefiting from Mauryan polish, and using a Hellenistic abacus of lotus and palmettes for decoration. The abacus would then adopt the Hamsa goose as an animal decorative symbol, in Lauria Nandangarh and the Rampurva lion. Sanchi and Sarnath would mark the culmination with four animals back-to-back instead of just one, and a new and sophisticated animal and symbolic abacus (the elephant, the bull, the lion, the horse alternating with the Dharma wheel) for the Sarnath lion.
Other chronological orders have also been proposed, for example based on the style of the Ashokan inscriptions on the pillars, since the stylistically most sophisticated pillars actually have the engravings of the Edicts of Ashoka of the worst quality (namely, very poorly engraved Schism Edicts on the Sanchi and Sarnath pillars, their only inscriptions). This approach offers an almost reverse chronological order to the preceding one. According to Irwin, the Sankissa elephant and Rampurva bull pillars with their Hellenistic abacus are pre-Ashokan. Ashoka would then have commissioned the Sarnath pillar with its famous Lion Capital of Ashoka to be built under the tutelage of craftsmen from the former Achaemenid Empire, trained in Perso-Hellenistic statuary, whereas the Brahmi engraving on the very same pillar (and on pillars of the same period such as Sanchi and Kosambi-Allahabad) was made by inexperienced Indian engravers at a time when stone engraving was still new in India. After Ashoka sent back the foreign artists, style degraded over a short period of time, down to the time when the Major Pillar Edicts were engraved at the end of Ashoka's reign, which now displayed very good inscriptional craftsmanship but a much more solemn and less elegant style for the associated lion capitals, as for the Lauria Nandangarh lion and the Rampurva lion.
Of the Allahabad pillar, only the abacus remains, the bottom bulb and the crowning animal having been lost. The remains are now located in the Allahabad Museum.
A few more possibly Ashokan capitals were also found without their pillars:
Kesariya (capital). Only the capital was found in the Kesaria stupa. It was discovered by Markham Kittoe in 1862, and said to be similar to the lion of the Lauriya Nandangarh pillar, except for the hind legs of the lion, which did not protrude beyond the abacus. 
Pillars of Ashoka