Judicial Review. I am confused on what it is.

So let’s assume for the moment Judicial Review doesn’t exist. Let’s also assume the federal constitution hasn’t change; it still contains the First Amendment.

Ohio passes a law that says a citizen can’t criticize the actions of a politician. Bob criticizes a politician and is arrested. The case eventually makes it to the U.S. Supreme Court.

Since Judicial Review doesn’t exist, must the court rule against Bob?

Absent judicial review, I don’t think that case even could end up before the Supreme Court of the United States. For that, you’d need a federal law, not a state one.

Not necessarily. After all, the claim by Bob is that the law of Ohio is unconstitutional. Assuming that appellate jurisdiction still exists in the Supreme Court, then the appeal is valid. The question of remedy, however, comes to the foreground, since the court would be precluded from “enforcing” its opinion regarding the law against the state of Ohio (the Court would lack what is called “potency”).

For an interesting review of judicial review and the possible alternatives, read Judicial Review and its Alternatives: An American Tale

What would be the point of a constitution if the embedded rights did not have the opportunity - in court - to trump (sorry) mere laws? You would have a situation like Britain, where the parliament could arbitrarily change anything by passing a new law… Presumably if the first amendment did not override state laws, if the court could not assert that fact, neither would division of powers between fed and states, nor any other constitutional provision. It would be a collection of suggestions, like the declaration of independence. “Freedom of speech? Yep, right up there with pursuit of happiness…”

I’m chipping in the information that judicial review of formal acts of the legislature (i.e., Acts of Congress in American terminology) is far from universal. Many jurisdictions don’t recognise it, and among them you will find well-established, firm democracies. Examples include the United Kingdom and Switzerland. In these jurisdictions, courts do not have the power to strikle down acts of the legislature for violation of constitutional law; they have to take the act for what it is (Switzerland being a special case in the sense that courts can strike down cantonal, i.e., state laws for violation of federal law including the federal constitution, but they can’t strike down federal laws). Britain, in particular, emphasises this doctrine very strongly under the heading of “sovereignty of Parliament”: Parliament can do anything it wants to without being bound by any rules superior to it.

In practice, the consequences are not as harsh as they sound in theory, because even in those jurisdictions courts can reduce the impact of statutes they don’t like by interpreting them very narrowly. But at least in theory, judicial review of statutes against the constitution is not universally affected.

What I said applies to judicial review of statutes against the constitution of the jurisdiction in question. But as AK84 said, the term is broader; it includes any scrutiny of an exercise of public power against the legal framework governing it. Administrative acts below the level of statutes are also subject to judicial review, both against constitutional and against statutory law; such judicial review is pretty universal in rule-of-law based systems, and takes place also in the United Kingdom and Switzerland.