The unparalleled biodiversity found in the American tropics (the Neotropics) has attracted the attention of naturalists for centuries. Despite major advances in recent years in our understanding of the origin and diversification of many Neotropical taxa and biotic regions, many questions remain to be answered. Additional biological and geological data are still needed, as well as methodological advances that are capable of bridging these research fields. In this review, aimed primarily at advanced students and early-career scientists, we introduce the concept of "trans-disciplinary biogeography," which refers to the integration of data from multiple areas of research in biology (e.g., community ecology, phylogeography, systematics, historical biogeography) and Earth and the physical sciences (e.g., geology, climatology, palaeontology), as a means to reconstruct the giant puzzle of Neotropical biodiversity and evolution in space and time. We caution against extrapolating results derived from the study of one or a few taxa to convey general scenarios of Neotropical evolution and landscape formation. We urge more coordination and integration of data and ideas among disciplines, transcending their traditional boundaries, as a basis for advancing tomorrow's ground-breaking research. Our review highlights the great opportunities for studying the Neotropical biota to understand the evolution of life.