The tasks of providing multi-decadal climate projections and seasonal plus sub-seasonal climate predictions are of significant societal interest and pose major scientific challenges. An outline is presented of the challenges posed by, and the approaches adopted to, tracing the possible evolution of the climate system on these various time-scales. First an overview is provided of the nature of the climate system's natural internal variations and the uncertainty arising from the complexity and non-linearity of the system. Thereafter consideration is given sequentially to the range of extant approaches adopted to study and derive multi-decadal climate projections, seasonal predictions, and significant sub-seasonal weather phenomena. For each of these three time-scales novel results are presented that indicate the nature (and limitations) of the models used to forecast the evolution, and illustrate the techniques adopted to reduce or cope with the forecast uncertainty. In particular, the contributions (i) appear to exemplify that in simple climate models uncertainties in radiative forcing outweigh uncertainties associated with ocean models, (ii) examine forecast skills for a state-of-the-art seasonal prediction system, and (iii) suggest that long-lived weather phenomena can help shape intra-seasonal climate variability. Finally, it is argued, that co-consideration of all these scales can enhance our understanding of the challenges associated with uncertainties in climate predictio
