There is hardly a more diverse family of birds in the world than the Cuculidae. The relationship of the groups of these birds to each other is still very uncertain. For now we'll consider them all one big happy family with seven distinctive subgroups. There are numerous questions about higher relationships within the cuckoos, and also plenty of questions at species level taxonomy.
Many mysteries still abound about cuckoos.
Many have distinctive vocalizations. Most recent arrangements do not include the Hoatzin among the Cuculiformes. I strongly recommend that birders learn all seven groups, and that you search for each as you enjoy birding the world. One this web page, we'll start with the three New World groups. This adult is bringing a large grasshopper to its nest, but roadrunners eat a wide variety of ground creatures, including snakes, lizards, and any bird it can run down.