The document discusses different types of routers and splitters in Mule, including collection splitters, message chunk splitters, scatter-gather, for each, and filters. Collection splitters split collections into individual messages while ensuring ordering, and message chunk splitters split messages into fixed-length chunks. Scatter-gather routes a message to multiple endpoints concurrently then aggregates the responses. For each splits a collection into elements and processes them iteratively. Filters allow filtering messages using expressions and optionally throwing exceptions.