Nanocrystals (NCs) doped with lanthanides are capable of efficient photon upconversion, i.e., absorbing long-wavelength light and emitting shorter-wavelength light. The internal processes that enable upconversion are a complex network of electronic transitions within and energy transfer between dopant centers. In this work, we study the rise and decay dynamics of upconversion emission from β-NaYF4 NCs codoped with Er3+ and Yb3+. The rise dynamics of the red and green upconverted emissions are nonlinear, reflecting the nonlinear nature of upconversion and revealing the mechanisms that populate the emitting states. The excited-state decay dynamics are nonexponential. We unravel the underlying decay pathways using photonic experiments. These reveal the contributions of different upconversion pathways visually, as each pathway exhibits a distinct response to systematic variation of the local density of optical states. Moreover, the effect of the local density of optical states on core-only NCs is qualitatively different from core-shell NCs. This is due to the different balance between feeding and decay of the electronic levels that produce upconverted emission. The understanding of the upconversion dynamics provided here could lead to better imaging and sensing methods relying on upconversion lifetimes or guide the rational optimization of the dopant concentrations for brighter upconversion.