Currently, there is little guidance for navigating measurement challenges that threaten construct validity in replication research. To identify common challenges and ultimately strengthen replication research, we conducted a systematic review of the measures used in the 100 original and replication studies from the Reproducibility Project: Psychology (Open Science Collaboration, 2015). Results indicate that it was common for scales used in the original studies to have little or no validity evidence. Our systematic review demonstrates and corroborates evidence that issues of construct validity are sorely neglected in original and replicated research. We identify four measurement challenges replicators are likely to face: a lack of essential measurement information, a lack of validity evidence, measurement differences, and translation. Next, we offer solutions for addressing these challenges that will improve measurement practices in original and replication research. Finally, we close with a discussion of the need to develop measurement methodologies for the next generation of replication research. Public Significance Statement Over the past decade, psychologists have been calling for methodological reform to increase the rigor and replicability of psychological science, which has been accompanied by progress in improving transparency and statistical practices. This article presents rigorous measurement practices as foundational for generating knowledge from psychological science that can be translated to inform policy, develop interventions, and improve people's lives. We review one of the largest sets of replication studies ever conducted to understand how measurement can be improved and discuss the need to develop measurement practices for the next generation of replication research.