Image compression is one of the most widely used groups of signal processing schemes in real-time applications. There are various algorithms for compressing images, each with pros and cons. Each method of data compression behaves differently for various types of data, thus a review of the common image algorithms seems necessary to compare the compression ratio, compression and decompression time, and generated file sizes. This paper aims to provide an insight into the characteristics of commonly used image-compression algorithms. Each algorithm is tested with controlled test images to determine the operational capabilities of each algorithm for different test cases. Subsequently, the performance of each algorithm is simulated and compared with other methods. Discussions on how algorithms behave with various test images are given in detail. The desired outcome of this study is a clear description of compression algorithms, and determining the suitability of each algorithm for different applications.