Digital watermarks have been proposed as the means for intellectual property right protection of multimedia data. Digital watermarking is a process of embedding information (or signature) directly into the media data by making small modifications. With the detection/extraction of the signature from the watermarked media data, digital watermarks can be used to identify the rightful owner, the intended recipients, as well as the authenticity of a media data [1,2]. Particularly, the watermark should still be detectable/extractable even after such common signal processing operations as digital-to-analog and analog-to-digital conversions, resampling, filtering, compression, geometric transformation, cropping, and etc applying to the watermarked image. In general, the embedding techniques can be classified into two categories: spatial domain approach or frequency domain approach. Many scholars have found that the frequency domain approach has some advantages because most of the signal processing operations can be well characterized in the frequency domain, and several good perceptual models are developed in the frequency domain [3]. Consequently, we focused our investigations on frequency domain approach by analyzing the robustness of the watermarked images that are created by Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) techniques, respectively. Besides the random keys, some researcher are exploring the data hiding technique to embed real logo images as the authentication. In this report, we will first outline the mathematical background of DCT and DWT watermarking techniques. Second, we will discuss and analyze the results of the watermarked images after multiple attacks. Third, we will discuss and implement a simple data hiding method. Finally, we will investigate the limitations of the watermarking techniques and discuss further research issues.