Acoustic Guitar Amplifiers - Choosing an acoustic guitar amplifier is not the same as choosing an electric guitar amplifier. Acoustic amps are meant to amplify the sound, make it louder without distorting the end result. With an electric amp you get a more distorted sound and they are lower definition, given the necessities of an electric guitar player.
The beauty of an acoustic guitar is the amount of tones and subtle richness in melodies it brings, so the goal of the player is to translate that same richness in a higher volume, to be able to express yourself in a venue where the traditional amplification form the guitar is not loud enough.
The first acoustic guitar amplifiers appeared back in the 80s with the name of Trace Acoustic combos, developed by Trace Elliot. Like all first models these were pretty expensive for the average player, but as time passed prices went down and more manufacturers started to develop their own high-definition amps.
When looking for an acoustic amp to buy, you'll need to consider quite a few things, including the desired volume you are going to set (especially taking into account the interaction with other instruments), the input you will need and the venue you are going to use it in. Many people forget to consider size, but this is a pretty important factor as you may need to easily transport your amplifier and place it in a spot on a stage. A big amp in a small stage can be really bothersome.
Some great amps out there that you can test are the Fender Acoustasonic Junior, AER Acousticube IIA and the Ibanez Troubadour 25. Give them a try if you find them at your local guitar shop.