Classical convergence theory of Runge–Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic degradation in accuracy known as order reduction, can arise. This talk will cover recent advancements in addressing order reduction for stiff, semilinear ODEs with an outlook towards broader classes of nonlinear problems. Notably, we do not need to resort to high stage order conditions nor fully implicit methods. We will explore the rich and interesting connections between new stiff order conditions and rooted trees. Numerical experiments confirm we can eliminate order reduction on a wide range of nonlinear ODEs using diagonally implicit Runge–Kutta methods with low stage order.