Integration is a key part of what Gartner termed 'post-modern ERP'. The premis is that your IT estate consists of a number of best of breed solutions, decoupled but integrated. The reality for most is that best of breed may be stretching it. At any sort of scale, even the best organisations tend to have a mixture of applications and infrastructure they love, and some they don't, but can't easily replace, the business case doesn't stack, or they simply have higher priority work to attend to.
Even during the heyday of the monolithic ERP this would have been the case for many. If your mega-vendor implementation takes five years, there will be legacy applications around for protracted periods of time.
So, what does a modern Integration Architecture look like? At it's heart, lies the Enterprise Service Bus - a completely unsexy piece of middleware designed to connect things to other things. Generally imbued with little direct business functionality, but the glue that binds.
The killer addition to the Enterprise Service Bus for larger organisations, is adding Master Data Management. MDM provides a single authoritative source of the 'reference' data within the organisation. As an example, not just all customers, but all customers with the correct attributes (name, address, contact details, company information), in the correct format. In this case, the ESB uses MDM in shuttling data between various systems and subsystems, ensuring data consistency and data quality.