In the last decade, cultural transmission experiments (transmission chains, replacement, closed groups and seeded groups) have become important experimental tools in investigating cultural evolution. However, these methods face important challenges, especially regarding the operationalization of theoretical claims. In this review, we focus on the study of cumulative cultural evolution, the process by which traditions are gradually modified and, for technological traditions in particular, improved upon over time. We identify several mismatches between theoretical definitions of cumulative culture and their implementation in cultural transmission experiments. We argue that observed performance increase can be the result of participants learning faster in a group context rather than effectively leading to a cumulative effect. We also show that in laboratory experiments, participants are asked to complete quite simple tasks, which can undermine the evidential value of the diagnostic criterion traditionally used for cumulative culture (i.e. that cumulative culture is a process that produces solutions that no single individual could have invented on their own). We show that the use of unidimensional metrics of cumulativeness drastically curtail the variation that may be observed, which raises specific issues in the interpretation of the experimental evidence. We suggest several solutions to these mismatches (learning times, task complexity and variation) and develop the use of design spaces in experimentally investigating old and new questions about cumulative culture.