Mainframes continue to be relevant due to their stability and ability to handle large data. They can interact with other technologies like Java and .NET through message queuing (MQ) as a mediator for data transfer. The process flow involves three layers - a frontend built on technologies like SharePoint, a backend on mainframes interacting with databases, and a web services layer transmitting requests between the frontend and backend via MQ. Requests are placed in MQ queues to trigger transactions that access databases, with responses returned in the same manner. While mainframes are an older technology, they remain necessary due to their dependability.