We have studied large, heterogeneous populations of discrete chemical oscillators (~100,000) to characterize two different types of density-dependent transitions to synchronized oscillatory behavior. For different chemical exchange rates between the oscillators and the surrounding solution, we find, with increasing oscillator number density, (1) the gradual Kuramoto synchronization of oscillatory activity or (2) the sudden quorum sensing "switching on" of synchronized oscillatory activity. We also describe the formation of phase clusters, where each cluster has the same frequency but is phase shifted with respect to other clusters, giving rise to a global signal that is more complex than that of the individual oscillators. Finally, we describe experimental studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators. A. F. Taylor et al., Science 323, 614 (2009). A. F. Taylor et al., Angewandte Chemie Int. Ed. 50, 10161 (2011). M. R. Tinsley et al., Nature Physics, doi:10.1038/nphys2371 (2012).