This multiple-manuscript dissertation explored the measurement invariance (MI) testing with multiple-group confirmatory factor analysis (MG-CFA) approach from different perspectives. Study 1 explored MI from a theoretical perspective by conducting a systematic review study on MI practices in education. The findings of this study indicated inconsistency in MI practices and showcased the limitations of the MI practices conducted by researchers in the field of education. Study 2 examined MI from an empirical perspective by implementing a cultural MI test of Strengths and Difficulties Questionnaires for elementary school students in the United States and China. The study provided a step-by-step demonstration of how to conduct an MI test appropriately. Study 3 investigated MI from a methodological perspective with a simulation study. This study examined the impact of model size and group size ratio on the sensitivity of fit measures to detect MI. The study found that model size, in combination with group size ratio, affected the power of CFI, RMSEA, and SRMR for identifying the metric or scalar noninvariance. Study 2 and Study 3 originated from the issues with MI practice identified from Study 1 and served as extensions of Study 1. These three manuscripts contributed to the research on MI testing with the MG-CFA approach theoretically, empirically, and methodologically. Overall, this series of studies help researchers gain a better understanding of the application of MI from different perspectives. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]