That really depends upon what oscilloscope you are using. Most modern oscilloscopes have the capability to continually stream data to a host computer. Bandwidth is an issue, so board based scopes (like the NI ones

) will allow you to stream at higher acquisition speeds. If you are using an NI scope, check out the example
niScope EX Fetch Forever.vi. IVI based scope APIs should use a similar mechanism. I can't comment on GPIB/SCPI based scopes, since I have not used that API for years.
Let us know a few more specifics - scope model, acquisition rate, API used, etc. - and we can help you more.