The majority of eukaryotic diversity is hidden in protists, yet our current knowledge of processes and structures in the eukaryotic cell is almost exclusively derived from multicellular organisms. The increasing sensitivity of molecular methods and growing interest in microeukaryotes has only recently demonstrated that many features so far considered to be universal for eukaryotes actually exist in strikingly different versions. In other words, during their long evolutionary histories, protists have solved general biological problems in many more ways than previously appreciated. Interestingly, some groups have broken more rules than others, and the Euglenozoa and the Alveolata stand out in this respect. A review of the numerous odd features in these 2 groups allows us to draw attention to the high level of convergent evolution in protists, which perhaps reflects the limits that certain features can be altered. Moreover, the appearance of one deviation in an ancestor can constrain the set of possible downstream deviations in its descendents, so features that might be independent functionally, can still be evolutionarily linked. What functional advantage may be conferred by the excessive complexity of euglenozoan and alveolate gene expression, organellar genome structure, and RNA editing and processing has been thoroughly debated, but we suggest these are more likely the products of constructive neutral evolution, and as such do not necessarily confer any selective advantage at all.