The article provides a comprehensive review of the theoretical aspects of Bose-Einstein condensation (BEC) in trapped gases. It covers the fundamental concepts, mean-field theory, and various properties of these systems, including density profiles, ground state configurations, collective oscillations, and thermodynamic functions. The review highlights how interactions between particles significantly modify the static and dynamic properties of the system, despite the dilute nature of the gases. It also discusses superfluidity, quantized vortices, and coherence effects such as the Josephson effect and interference phenomena. The accuracy and limitations of mean-field theory are assessed, and the paper concludes with a discussion on future perspectives in the field.The article provides a comprehensive review of the theoretical aspects of Bose-Einstein condensation (BEC) in trapped gases. It covers the fundamental concepts, mean-field theory, and various properties of these systems, including density profiles, ground state configurations, collective oscillations, and thermodynamic functions. The review highlights how interactions between particles significantly modify the static and dynamic properties of the system, despite the dilute nature of the gases. It also discusses superfluidity, quantized vortices, and coherence effects such as the Josephson effect and interference phenomena. The accuracy and limitations of mean-field theory are assessed, and the paper concludes with a discussion on future perspectives in the field.