The Gaia mission has opened a new window into the internal kinematics of young star clusters at the sub-km/s level, with implications for our understanding of how star clusters form and evolve. We use a sample of 28 clusters and associations with ages from 1-5 Myr, where lists of members are available from previous X-ray, optical, and infrared studies. Proper motions from Gaia DR2 reveals that at least 75% of these systems are expanding; however, rotation is only detected in one system. Typical expansion velocities are on the order of ~0.5 km/s, and, in several systems, there is a positive radial gradient in expansion velocity. Systems that are still embedded in molecular clouds are less likely to be expanding than those that are partially or fully revealed. One-dimensional velocity dispersions, which range from 1 to 3 km/s, imply that most of the stellar systems in our sample are supervirial and that some are unbound. In star-forming regions that contain multiple clusters or subclusters, we find no evidence that these groups are coalescing, implying that hierarchical cluster assembly, if it occurs, must happen rapidly during the embedded stage.