The Kardar-Parisi-Zhang (KPZ) fixed point is the universal scaling limit for a broad class of one-dimensional stochastic growth models, including the totally asymmetric simple exclusion process (TASEP). In this talk, I will present the transition probability of TASEP in half-space starting with a general deterministic initial condition. Applying the 1:2:3 KPZ scaling limit to this result yields an explicit formula for the half-space KPZ fixed point. Finally, we will discuss a connection between the half-space KPZ fixed point and a system of integrable coupled PDEs.