In this paper we provide a detailed description of Reed-Solomon (RS) codes, the most important algorithms for decoding them, and their use in concatenated coding systems for space applications. In the current literature there is scattered information regarding the bit-level implementation of such codes for either space systems or any other type of application. Consequently, we start with a general overview of the channel coding systems used in space communications and then we focus in the finest details. We first present a detailed description of the required algebra of RS codes with detailed examples. Next, the steps of the encoding and decoding algorithms are described with detail and again with additional examples. Next, we focus on a particularly important class of concatenated encoders/decoders namely the Consultative Committee for Space Data Systems (CCSDS) concatenated coding system that uses RS as the outer code, and a convolutional inner code. Finally, we perform a thorough performance evaluation of the presented codes under the AWGN channel model.