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Delay estimation in direct-sequence code-division multiple-access (DS-CDMA) systems is necessary for accurate code synchronization and for applications such as mobile phone positioning. Multipath propagation is among the main sources of error in the DS-CDMA delay estimation process, together with multiple access interference and non-line-of-sight (NLOS) propagation. This paper provides a review of main delay estimation techniques, existing in the literature so far, which are able to cope with multipath propagation, together with our novel delay estimation techniques proposed in the context of DS-CDMA systems. The performance of all these techniques is compared through analysis and simulations, considering also their relative computational complexity and required prior information. Starting from the traditional delay locked loops (DLL) and their improved variants, we discuss several recently introduced delay estimation techniques able to cope with multipath propagation. The characterization of these methods is given in a unified framework, suited for both rectangular and root raised cosine pulse shapes. The main focus in the performance comparison of the algorithms is on the closely-spaced multipath scenario, since this situation is the most challenging for achieving diversity gain with low delay spreads and for estimating LOS component with high accuracy in positioning applications.