Steganography is the science that deals with hiding of secret data in some carrier media which may be image, audio, formatted text or video. The main idea behind this is to conceal the very existence of data. We will be dealing here with image steganography. Many algorithms have been proposed for this purpose in spatial & frequency domain. But in almost all the algorithms it has been noticed that as we embed the secret data in the image the certain characteristics or statistics of the image get disturbed. Based on these disturbed statistics steganalysts can get the reflection about the existence of secret data which they further decode with the help of available steganalytic tools. Steganalysis is a science of attacking the hidden data to get an authorized access. Although steganalysis is not a part of this work but it may be sometimes discussed as a part of literature. Even in steganography we are not purely concerned with spatial or frequency domain rather our main emphasis is on adaptive steganography or model based steganography. Adaptive steganography is not entirely a new branch of steganography rather it is based upon spatial & frequency domain with an additional layer of mathematical model. So here we will be dealing with adaptive steganography which take care about the important characteristics & statistics of the cover image well in advance to the embedding of secret data so that the disturbance of image statistics as mentioned earlier, which attracts the forgery or unauthorized access, can be minimized. In this survey we will analyze the various steganography algorithms which are based upon certain mathematical model or in other words algorithms which come under the category of model based steganography.