Scientists and Engineers (LWR)
Scientists
XCOM starts with 10 scientists and may acquire more throughout the campaign.
Each scientist increases the speed of research by 2% (stacks additively).
An exact formula for research speed can be found here: Research
Scientists are also required in order to build laboratories. The first requires 20 scientists. Each subsequent laboratory requires double the number of scientist of the previous (e.g. the 4th lab requires 160 scientists).
Engineers
XCOM starts with 10 engineers and may acquire more throughout the campaign.
The speed to produce an item is reduced with more engineers. An exact formula can be found here: Engineering - Item Production Speed
Engineers are also required in order to build workshops. The first requires 20 engineers. Each subsequent workshop requires double the number of engineers from the previous (e.g. the 4th workshop requires 160 engineers).
The same engineer requirements apply to building satellite uplinks and nexuses. However, the first uplink (the one you start with) does not count towards this requirement. Also, both uplinks and nexuses share the engineer requirements and are independent from the workshop engineer requirements.