Normally, courts prohibit witnesses from testifying based on their own opinions or analysis. See Federal Rule of Evidence 602. Courts relax these rules for expert witnesses testifying about matters within their field of expertise.
Generally speaking, experts may testify about their conclusions in a case so long as their analysis is scientifically sound. In reaching their conclusions, experts may rely on the same sorts of evidence that people in their profession normally rely on in their work, even if the evidence is otherwise inadmissible in court. For example, a doctor may testify about his analysis of X-rays, even though the X-rays would normally be hearsay. See Rule 703 of the Federal Rules of Evidence.
Expert Testimony in the Federal Courts
In the federal courts, judges determine the credibility of expert witnesses in a pre-trial Daubert hearing. See Daubert v. Merrell Dow Pharmaceuticals, 509 U.S. 579 (1993). In considering witnesses' qualifications, judges may consider information that is not admissible as evidence.
Before trial, all experts must prepare a report summarizing their analysis and conclusions, and share the report with all other parties. See disclosure; Rule 26(a) of the Federal Rules of Civil Procedure. This allows other parties to effectively cross-examine the expert.
Expert testimony is not limited to matters beyond the understanding of the ordinary juror. Instead, experts may testify on any subject within their area of expertise so long as their testimony will assist the jury. See Rule 702.