Massive multi-user (MU) multiple-input multiple-output (MIMO) will be a core technology in next-generation wireless systems. By equipping the infrastructure base-stations (BSs) with hundreds of antenna elements and serving tens of user equipments (UEs) in the same time-frequency resource, massive MU-MIMO enables orders-of-magnitude higher spectral efficiency than existing wireless systems. The presence of large number of antenna elements at the BS, however, causes significant implementation challenges. In particular, optimal data detection at the BS that maximizes the spectral efficiency (i.e., the number of bits that can be transmitted reliably over a given bandwidth) entails prohibitive complexity. As a result, the majority of existing data detection algorithms for massive MU-MIMO and corresponding hardware designs are sub-optimal, thereby sacrificing spectral efficiency. In this thesis, we will provide a positive answer to the question "Is optimal data detection in massive MU-MIMO systems feasible?'" by considering a multidisciplinary research approach that spans theory, algorithm development, and application-specific integrated circuit (ASIC) design. Concretely, we will propose a range of solutions on theory, algorithm, and hardware level that enable optimal data detection in practice. In addition, we will present new methods that reduce the complexity of channel-matrix preprocessing, as well as novel architectures and algorithms that enable parallel processing of the most critical tasks in massive MU-MIMO BSs. In order to demonstrate the effectiveness of all our solutions in practically-relevant communication scenarios, we will support our findings via theoretical results, numerical simulations, and ASIC implementations.