Hyperspectral image compression has received considerable interest in recent years due to enormous data volumes collected by imaging spectrometers which consists of hundreds of contiguous spectral bands with very high between-band spectral correlation. Due to such significantly improved spatial and spectral resolution provided by a hyperspectral imaging sensor, hyperspectral imagery expands the capability of multispectral imagery in many ways, such as subpixel target detection, object discrimination, mixed pixel classification, material quantification, etc. It also presents new challenges to image analysts, particularly, how to effectively deal with its enormous data volume so as to achieve their desired goals. One common practice is to compress data prior to image analysis. Two types of data compression can be performed, lossless and lossy in accordance with redundancy removal. More specifically, lossless data compression is generally considered as data compaction which eliminates unnecessary redundancy without loss of information. By contrast, lossy data compression removes unwanted information or insignificant information which results in entropy reduction. Which compression should be used depends heavily upon various applications. For example, in medical imaging, lossless compression is preferred to lossy compression in order to avoid potential lawsuits against doctors. However, in this case, only small compression ratios can be achieved, generally less than 3:1. On the other hand, video processing such as HDTV (High Definition TV) can benefit from lossy compression. For remotely sensed imagery, both types of compression can be beneficial and have been studied and investigated extensively in the past [1-8]. Since we are interested in exploitation-based applications, data analysis is generally determined by features of objects in the image data rather than the image itself As a result, lossless compression may not offer significant advantages over lossy compression in the sense of feature extraction. So, in this chapter the main interest will be focused on lossy hyperspectral image compression. The success of a lossy compression technique is generally measured by whether or not its effectiveness meets a preset desired goal which in turn determines which criterion should be used for compression. As an example. Principal Components Analysis (PCA) is a compression technique that represents data in a few principal components determined by data variances [9-10]. Its underlying assumption is based on the fact that the data are wellrepresented and structured in terms of variance, where most of data points are clustered and can be packed in a low dimensional space. Unfortunately, it was recently shown in [11-13] that Signal-to-Noise Ratio (SNR) was a better measure than data variance to measure image quality in multispectral imagery. Similarly, the Mean Squared Error (MSE) has been also widely used as a criterion for optimality in communications and signal processing such as quantization. However, it is also known that it may not be appropriate to be used as a measure of image interpretation. This is particularly true for hyperspectral imagery which can uncover many unknown signal sources, some of which may be very important in data analysis such as anomalies, small targets which generally contribute very little to SNR or MSE. In the PCA these targets may only be retained in minor components instead of principal components. So, preserving only the first few principal components may lose these targets. In SNR or MSE, such targets may very likely be suppressed by lossy compression if no extra care is taken since missing these targets may only cause inappreciable loss of signal energy or small error. By realizing the importance of hyperspectral data compression, many efforts have been devoted to design and development of compression algorithms for hyperspectral imagery. Two major approaches have been studied. One is a direct extension of 2D image compression to 3D image compression where many 2D image compression algorithms that have proven to be efficient and effective in 2D images are extended to 3D algorithms. Another is spectral/spatial compression which deals with spectral and spatial compression separately. While the former considers a hyperspectral image as an image cube as a whole, the latter performs spectral/spatial compression on a hyperspectral image with ID compression on spectral information and 2D compression on spatial information. Despite a hyperspectral image can be considered as an image cube, a direct application of 3-D image compression to such a 1-D spectral/2-D spatial image cube may not be applicable in some cases as shown by examples. This is largely due to the fact that the spectral correlation of a hyperspectral image cube provides more crucial information than the spatial information in many exploitation-based applications. Therefore, an effective hyperspectral image compression technique must be able to explore and retain critical spectral information while the images are compressed spatially. This paper investigates these two approaches and provides evidence that 3D compression does not necessarily perform better than spectral/spatial compression in hyperspectral image compression from an exploitation point of view. In particular, using MSE or SNR as a compression criterion may result in significant loss of spectral information in data analysis. Additionally, in many cases, separating spectral and spatial compression may achieve better results in terms of preserving spectral information that is crucial in hyperspectral data exploitation. In order to demonstrate that it is indeed the case, this chapter studies various scenarios via a synthetic image simulated by a real HYperspectral Digital Image Collection Experiment (HYDICE) image to show that a simple spectral/spatial compression technique may perform as well as or even better than 3D lossy compression. Finally, we further develop several PCA-based spectral/spatial hyperspectral image compression techniques for hyperspectral image compression which are easy to implement, but yet achieve at least same results than a 3D lossy compression technique that is extended from its 2D compression counterpart. Experiments show that the proposed spectral/spatial hyperspectral image compression generally performs better than standard 3D hyperspectral image compression. The remainder of this chapter is organized as follows. Section 2 reviews two well-known 2D image compression techniques, wavelet-based JPEG 2000 and set partitioning in hierarchical tree (SPIHT), and their extensions to 3D compression. Section 3 develops two principal components analysis (PCA)-based spectral/spatial compression techniques for hyperspectral image compression, referred to as Inverse PCA (IPCA)/spatial compression and PCA/spatial compression. Section 4 demonstrates that 3D lossy compression does not necessarily perform better than the PCA-based spectral/spatial compression techniques in terms of mixed pixel classification via experiments. Section 5 conducts real image experiments for comparative analysis. Finally, Section 6 concludes with some remarks.