Plant species differ in many functional traits that drive differences in rates of photosynthesis, biomass allocation, and tissue turnover. Yet, it remains unclear how -- and even if -- such traits influence whole-plant growth, with the simple linear relationships predicted by existing theory often lacking empirical support. Here we present a new theoretical framework for understanding the effect of diverse functional traits on plant growth and shade-tolerance, extending a widely-used theoretical model that links growth rate in seedlings with a single leaf trait to explicitly include influences of size, light environment, and five other prominent traits: seed mass, height at maturation, leaf mass per unit leaf area, leaf nitrogen per unit leaf area, and wood density. Based on biomass production and allocation, this framework explains why the influence of prominent traits on growth rate and shade tolerance often varies with plant size and why the impact of size on growth varies among traits. Considering growth rate in height, we find the influence of: i) leaf mass per unit leaf area is strong in small plants but weakens with size, ii) leaf nitrogen per unit leaf area does not change with size, iii) wood density is present across sizes but is strongest at intermediate sizes, iv) height at maturation strengthens with size, and v) seed mass decreases with size. Moreover, we show how traits moderate plant responses to light environment and also determine shade tolerance, supporting diverse empirical results. By disentangling the effects of plant size, light environment and traits on growth rates, our results provide a solid theoretical foundation for trait ecology and thus provide a platform for understanding growth across diverse species around the world.