Depends what you're doing. Most smaller surface-mount components and these days even a lot of standardized through-hole components can be assembled via pick and place machines and reflow ovens, which are largely automated. Larger components may require some extra steps like a small blob of glue to fix them in place - this comes up a lot for edge connectors, switches, or other larger mechanical components where the weight distribution doesn't allow them to rest flat on the board during reflow. Larger through-hole devices might need assistance with initial insertion or may be paired to other mechanical interfaces like a heatsink which requires some manual interaction. In some cases (particularly for boards with through-hole components all on one side) the soldering step can be automated by wave soldering. There's still some constraints on what can be automated, but it's all a lot less manual than the 90s/00s.
Some components, particularly transformers, might also be constructed by hand for custom/complex structures. That's component assembly rather than board assembly, but it's a consistent source of manual labor involvement in the supply chain.
Design for manufacturability is one of the important goals being considered in any PCB design. High-volume or low-cost boards will optimize for automated assembly and find ways to substitute or eliminate components with higher assembly costs. Extremely high-volume boards like in smartphones can justify custom tooling if it helps automate assembly.
Some components, particularly transformers, might also be constructed by hand for custom/complex structures. That's component assembly rather than board assembly, but it's a consistent source of manual labor involvement in the supply chain.
Design for manufacturability is one of the important goals being considered in any PCB design. High-volume or low-cost boards will optimize for automated assembly and find ways to substitute or eliminate components with higher assembly costs. Extremely high-volume boards like in smartphones can justify custom tooling if it helps automate assembly.