Among the existing lossy compression methods, the transform coding is one of the most effective strategies. The Discrete Wavelet Transform (DWT) can be efficiently used in image coding applications because of its advantages as compared to the other transforms. A typical wavelet image compression system is composed of three connected components namely transformation, quantization and coding. In this paper, we review the recent improvements of each component. We present a detailed study of the recent implementation of the DWT as well as of its improvements. In addition, we describe the main principles of the wavelet-based compression schemes such as EZW, SPIHT, SPECK and EBCOT. We review the advantages and shortcomings of each of these algorithms. Also, we provide a survey of the recent improvements of the different coding schemes. Moreover, a comparative analysis of the recent enhancement and compression techniques is carried out in terms of visual quality and encoding time. We conclude by some guidelines which concern the design of an efficient codec for wavelet image compression using spline transform and improved coding scheme.