While there have been remarkable advances in recent years in the areas of both coding and detection for data storage, this book focuses on data detection, or the processing of reading back waveforms to reproduce stored data, in conjunction with the traditional modulation coding method called run-length-limited or (d, k) coding. Among notable recent advances in the area of data detection is the application of the Viterbi algorithm combined with partial response linear equalization, known as partial response maximum likelihood (PRML), to commercial magnetic disk drives. The decision feedback equalizer (DFE), a well established data detection technique in communication channels subject to intersymbol interference (ISI), has also attracted attention in the magnetic recording community. One of the objectives of this book is to provide a tutorial review of the application of these detection schemes to magnetic recording. Philosophies behind these detection schemes are explained, as well as methods for analyzing their performance. Performance of these detection schemes is compared with that of the traditional peak detection method to provide insight into density improvements that can be achieved using these schemes. The main emphasis of the book is on the more recent idea proposed by the authors, namely, the application of fixed delay tree search (FDTS) to high density magnetic recording. Although the idea of depth-limited tree search has long existed in coding and in detection for ISI channels, it has not been previously noted that, for certain constrained ISI channels, depth-limited tree search yields an asymptotically optimal performance. This book explores the idea of depth-limited search on constrained channels and shows how a relatively simple FDTS detector combined with DFE, called FDTS/DF, achieves a near-optimal performance when applied to high density magnetic recording where the minimum run-length constraint may be required to suppress nonlinearities and media noise.