Image compression is an important methodology to compress different types of images. In modern days, as one of the most fascinating machine learning techniques, the authors have applied the idea of Deep Learning in different cases of Neural Networks to prove and justify that it is the most flexible method to analyze and compress the images. Different types of neural networks are available such as Deep Neural Network (DNN), Convolutional Neural Network (CNN), Binarized Neural Networks (BNN), Artificial Neural Networks (ANN) to perform image compression. So, in this review paper the authors have discussed how deep learning concept is applied on different types of Neural Networks in order to achieve image compression of perfect qualities with proper image classifications. In order to obtain that proper image classification, ther is a need for deep learning on DNN, CNN, BNN, ANN and apply the same concept in different types of images in a justified manner with difference of analysis. This is called compression technique based on conceptual analysis of images.