Difference-in-Difference is one of the most popular quasi-experimental techniques, backed by a large body of historical evidence.
Regression Discontinuity Design is a quasi-experimental design and another way to deal with selection bias.
It is often not possible to do a randomized controlled trial or RCT in a real-world setting for impact evaluation.
Propensity Score Matching (PSM) has been used since the 1980s to reduce selection bias and produce better causal estimates.