The main models
Single-blind is the traditional default in much of the sciences: reviewers know who the authors are, authors do not know the reviewers. The reviewer's anonymity is intended to let them be candid without fear of reprisal.
Double-blind hides both. Authors do not know reviewers, and reviewers are not told who the authors are. It is standard in much of the social sciences and humanities and is increasingly offered as an option elsewhere.
Open review makes identities known, and sometimes publishes the reports alongside the paper. Variants differ — some reveal identities only after acceptance, some publish signed reports, some publish anonymous reports.
A fourth pattern is transparent or post-publication review, where the paper appears first and review happens in the open afterwards. It is a minority model but growing.
Double-blind hides the authors from reviewers. Single-blind does not — which is the argument at the centre of the debate.
The trade-offs
The case for double-blind is that knowing an author's identity lets reputation, institution, nationality and gender influence assessment. Studies of this have produced mixed but not negligible findings, and the concern is taken seriously enough that many journals now offer it.
The case against is that true blinding is often impossible. In a specialised subfield the topic, method and self-citations identify the group anyway, and partial blinding may be worse than none — it can create a false sense that bias has been removed.
Open review argues that accountability improves quality: a signed report is a considered report. The counterargument is power. A junior reviewer asked to criticise a senior figure by name is in a different position than an anonymous one, and open review may simply suppress the criticism.
What changes for you
As an author under double-blind, you must actually anonymise. Remove names and affiliations, strip identifying metadata from the file, and handle self-citation in the third person — "as shown in [12]" rather than "in our previous work". Journals return manuscripts that fail this.
As a reviewer, adjust what you can infer. Under double-blind you cannot weigh a group's track record, and you should not try to work out who the authors are.
Check the model before submitting, since it is not always obvious from the journal homepage, and some journals let the author choose. If you have a reason to prefer one — an early-career researcher without an established name, for instance — that is a legitimate factor in choosing where to submit.