Quasi-experimental research designs have partial control over independent variables, do not use randomized populations, and are categorical in nature. They have advantages of being more natural, provoking fewer concerns about external validity, and being more resource-efficient and realistic, but have disadvantages of lower internal validity, less manipulation, and increased confounding variables. The main types are person-by-treatment quasi-experiments, which maintain partial control and use random assignment in laboratories, and natural experiments, which do not use true random assignment but instead utilize phenomena for comparison.