A written request served on another party to admit certain facts as being true or documents as being genuine. If the admission is made, an issue can often be removed from the litigation. Request for admissions are relatively cheap, but are more expensive than requests for production or interrogatories because requests for admissions have to be individually tailored to the facts of each case. They give you some leverage in recovering certain costs and expenses if the request should have been admitted but was instead denied. A deposition live testimony under oath of any person who knows anything about the case.
Every lawyer involved with the case can ask questions of the witness, just like at trial.
Live testimony of any witness or party lets the lawyers see how witnesses will testify and how they appear. As such, it's great rehearsal for trial and the only chance your lawyer has to evaluate the quality of the witnesses. It's the only discovery device available to get testimony or documents from non-parties. If the witness dies or is unavailable for trial, the deposition can be used instead of live testimony. Travel is often required, since you cannot require a witness to be deposed anywhere farther than 150 miles from home.