Digital image watermarking provides security, copyright protection, and authenticity to multimedia content by embedding digital content like text, image, and video. In the modern digital age, watermarking of digital images is an essential aspect of providing authenticity to digital content. Digital image watermarking is also used for the authenticity of the medical image in telemedicine applications. In these applications, digital image watermarking provides security to various medical images like Computerized tomography (CT) scans, Magnetic resonance imaging (MRI) images, and X-radiation (X-ray) images. In the past decades, many intellectuals have been working in the field of image watermarking to provide various characteristics features to watermarking like sufficient embedding capacity, strong robustness, and better imperceptibility. This paper covers watermarking techniques based on Schur decomposition and various types of moments like Zernike moment, Fourier harmonic moments, polar harmonic moments, etc. A survey on watermarking techniques suitable for telemedicine applications which include various medical images like CT-scan, MRI image, and X-ray images, is also presented. Various performance measures proposed by different researchers are also discussed, and the suitability of these measures for watermarking schemes is analysed under various attacks. In this paper, novel classification of watermarking schemes, recent essential requirements for different categories of image watermarking applications are covered. A tabular comparison of various watermarking schemes based on different families of moments are presented and also a comparative analysis of outcomes of different categories of moment based watermarking schemes is included. Various challenges and opportunities are also included to make this review more comprehensive.