Increasing demands on the high capacity wavelength division multiplexed (WDM) transmission system now require newly developed transmission windows beyond the gain bandwidth supported by erbium-doped fiber amplifiers (EDFA). With the intensive development efforts on new rare-earth dopants and fiber nonlinearity (Raman process) for fast few years, wideband optical amplifiers now can support easily over 4-5 fold wider gain bandwidth than it was formerly possible with the conventional EDFAs. Of various breeds for this application, there exist three distinct approaches near 150nm band, accessible in the commercial market. These include: Thulium-doped fluoride fiber amplifiers (TDFA) for S+band (1450-1480 nm) and S band (1480-1530 nm), EDFAs for C band (1530-1560nm) and L band (1570-1610nm) and L band (1570-1610nm), Raman amplifiers with 100 nm's of gain bandwidth (with flexible location from S+ to L Band), and hybrid amplifiers with serial/parallel combinations of above techniques. Even though there have been much increased experimental reports for all of these amplifiers, the complexity of the amplification dynamics from the number of involving energy levels and difficulty in measuring experimental parameters make it harder than ever to predict the performance of wideband amplifiers in general. This lack of serious study on the analytic or numerical analysis on wideband amplifiers could cause the future impairments for the prediction and estimation of the amplifier performances for different applications, restricting the successful deployment of wideband amplifier based transmission systems. In this paper, we present the numerical model and analysis techniques for wideband amplifiers (C/L band EDFA, Raman amplifier, and TDFA),along with their application examples.