Wavelets are being suggested as a platform for various tasks in image processing. The advantage of wavelets lie in its time frequency resolution. The use of different basis functions in the form of different wavelets made the wavelet analysis a destination for many applications. The performance of a particular technique depends on the wavelet coefficients arrived after applying the wavelet transform. The coefficients for a specific input signal depends on the basis functions used in the wavelet transform. Hence, in this paper toward this end, different basis functions and their features are presented. As many image comprssion algorithms base on wavelet transform, selection of basis function for image compression should be taken with care. In this paper, the factors influencing the performance of image compression are presented. In addition to this, a broad review of wavelets in image processing applications and selection of basis function for different image processing tasks are presented.