I have written before about the advantages of a hosted model of eDiscovery. A closely related model is Software as a Service (SaaS) where the eDiscovery application is delivered from a remote, third-party application server. The software vendor owns the software, hardware and support services that it delivers to the customer.
A SaaS vendor may or may not also host the data that uses the SaaS. Many SaaS products originate at the vendor's application servers and are delivered over high speed WAN connections to the customer site. Other SaaS products are set up for hosted data that is located within the vendor location, with customers running the application from their client machines on the remote hosted data.
The latter is the more common model within eDiscovery. I would not go so far as to call hosting and SaaS the same thing, they're not. But they are so deeply entwined in the eDiscovery world that you will often hear them used synonymously. I don't consider this a large semantic problem, just be aware that SaaS as an application delivery medium does not require that data be hosted at a remote site.
How does SaaS impact eDiscovery? I have written before about the large amount of press devoted to eDiscovery activities within the corporate firewall. I certainly support many of these activities because they dovetail with good storage hygiene and can improve information management. But when you start moving into the realm of legal review and processing, then you are moving away from most corporate competence. Analytics and basic machine-based review is very helpful for ECA and simple matters. But complex and/or frequent matters require much more intensive analysis, review and processing. This is the competence of the large law firms who specialize in handling civil cases for their corporate customers.
This is the realm of the hosted eDiscovery vendor who runs eDiscovery software (i.e., SaaS) on their customer's data. In this model, the vendor secures collected data in a highly secure hosted infrastructure. The vendor also provides an eDiscovery SaaS to its customers to process and analyze data, and to provide tiered views, tagging and access rights to potentially hundreds of different reviewers. The corporation and its law firms can use the eDiscovery SaaS from their own workstations, commonly from their browser. If it wishes (or if the judge says so) the corporation can grant highly controlled access rights to a variety of users: corporate employees, law firms, co-defendants, government agencies, even opposing counsel when appropriate. Through the eDiscovery SaaS access control and secure screens, the corporation can control what information is presented to whom.