The climate change experiments under the fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), namely the twentieth century simulations (20C3M) and Special Report on Emissions Scenarios (SRES) A1B, are revisited to study whether these models can reproduce the ENSO and ENSO Modoki patterns as the two important modes from statistical linear analysis as observed. The capability of the models in simulating realistic ENSO/ENSO Modoki teleconnections with the Indian summer monsoon, and also the implications for the future are also explored. Results from the study indicate that only ~1/4th of the models from 20C3M capture either ENSO or ENSO Modoki pattern in JJAS. Of this 1/4th, only two models simulate both ENSO and ENSO Modoki as important modes. Again, out of these two, only one model simulates both ENSO and ENSO Modoki as important modes during both summer and winter.It is also shown that the two models that demonstrate ENSO Modoki as well as ENSO associated variance in both 20C3M and SRESA1B represent the links of the ISMR with ENSO reasonably in 20C3M, but indicate opposite type of impacts in SREA1B. With the limited skills of the models in reproducing the monsoon, the ENSO and ENSO Modoki, it is difficult to reconcile that the teleconnections of a tropical driver can change like that. All these indicate the challenges associated with the limitations of the models in reproducing the variability of the monsoons and ENSO flavors, not to speak of failing in capturing the potential impacts of global warming as they are expected to. More research in improving the current day simulations, improving model capacity to simulate better by improving the Green House Gases (GHG) and aerosols in the models are some of the important and immediate steps that are necessary.