Terrestrial ecosystems sequester roughly 30% of anthropogenic carbon emission. However this estimate has not been directly deduced from studies of terrestrial ecosystems themselves, but inferred from atmospheric and oceanic data. This raises a question: to what extent is the terrestrial carbon cycle intrinsically predictable? In this paper, we investigated fundamental properties of the terrestrial carbon cycle, examined its intrinsic predictability, and proposed a suite of future research directions to improve empirical understanding and model predictive ability. Specifically, we isolated endogenous internal processes of the terrestrial carbon cycle from exogenous forcing variables. The internal processes share five fundamental properties (i.e., compartmentalization, carbon input through photosynthesis, partitioning among pools, donor pool-dominant transfers, and the first-order decay) among all types of ecosystems on the Earth. The five properties together result in an emergent constraint on predictability of various carbon cycle components in response to five classes of exogenous forcing. Future observational and experimental research should be focused on those less predictive components while modeling research needs to improve model predictive ability for those highly predictive components. We argue that an understanding of predictability should provide guidance on future observational, experimental and modeling research.