The paper examines methods and limitations for generating entangled states of trapped atomic ions, focusing on quantum logic operations as the central mechanism for creating entanglement. It discusses experimental issues related to the proposal for trapped-ion quantum computation by J. Cirac and P. Zoller, identifying several possible decoherence mechanisms and their significance. The paper also explores potential applications of entangled states of trapped ions beyond quantum computation, such as quantum correlations, simulations, and mass spectrometry. Key topics include laser cooling, generation of nonclassical states, quantum logic, and decoherence mechanisms, including motional and internal state decoherence. The authors aim to provide a comprehensive analysis of the practical limits of coherent control methods for trapped ions, particularly in the context of quantum logic and computation.The paper examines methods and limitations for generating entangled states of trapped atomic ions, focusing on quantum logic operations as the central mechanism for creating entanglement. It discusses experimental issues related to the proposal for trapped-ion quantum computation by J. Cirac and P. Zoller, identifying several possible decoherence mechanisms and their significance. The paper also explores potential applications of entangled states of trapped ions beyond quantum computation, such as quantum correlations, simulations, and mass spectrometry. Key topics include laser cooling, generation of nonclassical states, quantum logic, and decoherence mechanisms, including motional and internal state decoherence. The authors aim to provide a comprehensive analysis of the practical limits of coherent control methods for trapped ions, particularly in the context of quantum logic and computation.