If you've ever seen video of a Foxconn factory you've seen the rows of people carefully placing ICs onto circuit boards. In fact, there are machines to do that. They're called pick and place machines[0]. They've existed for many years. But labor in China is cheap enough that it often makes more sense to pay humans to do it manually than to invest in automation.
There are several types of components that require surface mounting on PCBs. By far the most common are things like resistors & capacitors that are machine placeable. But others, like BGAs and through-hole components, often require hand placement because they require hand soldering and can't go through a wave solder machine. Additional possible complications are boards with components placed on both sides, or multi-layer boards with non-standard solder. Finally, Debug/Repair stations are always manual.
Source: Masters in operations research and 15 years experience writing factory control software for one of Foxconn's direct competitors & largest trading partners.
PS: There are also at least demos of pick and place for through-hole components. But, I don't know how production ready they are. (Manufacturing PCBs is not my area.)
Through hole components are commonly hand placed or hand soldered because there are only a few on the board, not enough to make machine placement/wave soldering cost effective. Additionally, some through hole components have shapes that make machine placement difficult.
"15 years" in operations and isn't even aware of this basic fact.
(Sibling comment is correct that SMT automated assembly is used for most parts, and a few large TH parts like connectors are soldered on at the end. Wire bondout of chips into chip packages and things like SD cards and USB sticks however seems to be more manual.)