This thesis examines the potentially achievable prediction skill of temperature and precipitation on interannual to decadal time scales by analyzing predictability in perfect-model experiments using coupled climate models. I develop a framework which (1) compares perfect‐model prediction experiments with predictions of the real world, and (2) assesses the added value from capturing the initial state in the climate system in decadal predictions. I find that for the annual average near‐surface air temperature, ideal initialization may substantially improve the predictions during the first two forecast years particularly in parts of the Southern Ocean, the Indian Ocean, the tropical Pacific and North Atlantic, and some surrounding land areas. On longer time scales, the predictions rely more on model performance in simulating low‐frequency variability and long‐term changes due to external forcing. This thesis also investigates conditional predictability dependent on initial states, in particular multi-year predictability conditional on the state of the El Niño–Southern Oscillation (ENSO) at the time of prediction initialization. I find that predictions starting with El Niño or La Niña conditions exhibit higher skill in predicting near-surface air temperature and precipitation multiple years ahead, compared to predictions initialized with neutral ENSO conditions. This thesis also compares the predictability for mean and extreme temperature and precipitation on interannual to decadal time scales. The results show that both the mean and likelihood of near-surface air temperature extremes are predictable in many regions in the first lead year, while the areas exhibiting precipitation predictability tend to be mostly located in low-latitude regions. On decadal time scales, significant potential prediction skill for mean and extreme temperatures is found over the North Atlantic and the Southern Ocean and also over some land areas. Indices of moderate temperature extremes tend to show a higher predictability than the mean. This work suggests potentially improvable skill of current decadal prediction systems under the assumption of idealized initialization and identifies climate states that enable more skillful predictions relative to other climate states. This will ultimately lead to improved decadal forecasts, something that is critical for decision-makers requiring information on climate parameters for future planning across a range of sectors, such as water and bushfire management and agriculture