Travel booking engines handle complex itineraries and bookings through:

. Multi-Segment Booking Options: Allows users to book multiple segments, such as flights, hotels, and car rentals, in a single transaction, accommodating complex travel plans.

. GDS Integration: Integrates with Global Distribution Systems (GDS) to access comprehensive travel content and availability, enabling the booking of complex itineraries with multiple components.

. Flexible Search and Filtering: Provides advanced search and filtering options to help users find and book complex itineraries based on various criteria, such as departure times, layovers, and accommodation types.

. Itinerary Management: Offers tools for managing and modifying itineraries, allowing users to view, edit, and track their bookings in one place.

. Dynamic Pricing and Availability: Adjusts pricing and availability in real-time based on the booking conditions and demand, ensuring accurate and up-to-date information.

Overall, multi-segment booking options, GDS integration, flexible search and filtering, itinerary management, and dynamic pricing are key methods for handling complex itineraries and bookings in travel booking engines.