In a situation where you have been retained or enlisted to serve as an expert witness, the other side will want to gather information that it will use to impeach your credibility should you testify. This information gathering is part of what is called the pre-trail discovery process and can be quite invasive. Depending on the case, the other side may want to see private emails/correspondence, comments from peer reviewers and even in some cases tax returns.
In most cases, draft expert reports and communications between you and the attorney on your side are shielded from discovery as protected attorney work-product. In addition, presumably your side’s counsel will also represent you through the other side’s discovery.
When disputes arise over the scope or depth of discovery into expert witnesses, they turn on factual circumstances such as the relevance of information sought, existence of privacy and privilege issues, how burdensome is the request and can the information be obtained by other, less intrusive means.