A large spread exists in both Indian and Australian average monsoon rainfall and in their interannual variations diagnosed from various observational and reanalysis products. While the multi model mean monsoon rainfall from 59 models taking part in the Coupled Model Intercomparison Project (CMIP3 and CMIP5) fall within the observational uncertainty, considerable model spread exists. Rainfall seasonality is consistent across observations and reanalyses, but most CMIP models produce either a too peaked or a too flat seasonal cycle, with CMIP5 models generally performing better than CMIP3. Considering all North-Australia rainfall, most models reproduce the observed Australian monsoon-El Nio Southern Oscillation (ENSO) teleconnection, with the strength of the relationship dependent on the strength of the simulated ENSO. However, over the Maritime Continent, the simulated monsoon-ENSO connection is generally weaker than observed, depending on the ability of each model to realistically reproduce the ENSO signature in the Warm Pool region. A large part of this bias comes from the contribution of Papua, where moisture convergence seems to be particularly affected by this SST bias. The Indian summer monsoon-ENSO relationship is affected by overly persistent ENSO events in many CMIP models. Despite significant wind anomalies in the Indian Ocean related to Indian Ocean Dipole (IOD) events, the monsoon-IOD relationship remains relatively weak both in the observations and in the CMIP models. Based on model fidelity in reproducing realistic monsoon characteristics and ENSO teleconnections, we objectively select 12 "best" models to analyze projections in the rcp8.5 scenario. Eleven of these models are from the CMIP5 ensemble. In India and Australia, most of these models produce 5-20 % more monsoon rainfall over the second half of the twentieth century than during the late nineteenth century. By contrast, there is no clear model consensus over the Maritime Continent.