There are some widely recognizes Presidential immunities from criminal and/or civil liability. Most importantly, there is absolute immunity from civil and criminal liability at any time (in office or afterwards) for the President's conduct of his official discretionary duties in an official capacity (judges, prosecutors and legislators have comparable immunities).

There might be some exceptions to this for violations of federal laws targeted at official capacity conduct (e.g. bribery, theft of government property, Posse Comitatus Act violations, etc.) if the prosecution is for official conduct after being removed from office.

But not under state laws (the state and federal cases are distinct due to the Supremacy Clause of the U.S. Constitution).

This clause sheds light on substantive immunity but not on immunity from prosecution or lack thereof prior to an impeachment conviction.

There are some widely recognizes Presidential immunities from criminal and/or civil liability. Most importantly, there is absolute immunity from civil and criminal liability at any time (in office or afterwards) for the President's conduct of his official discretionary duties in an official capacity (judges, prosecutors and legislators have comparable immunities).

There might be some exceptions to this for violations of federal laws targeted at official capacity conduct (e.g. bribery, theft of government property, Posse Comitatus Act violations, etc.) if the prosecution is for official conduct after being removed from office. But the Supremacy Clause of the U.S. Constitution probably bars criminal prosecutions for the official misconduct of a President while in office under state law.

There might be some exceptions to this for violations of federal laws targeted at official capacity conduct (e.g. bribery, theft of government property, Posse Comitatus Act violations, etc.) if the prosecution is for official conduct after being removed from office (the impeachment language of the U.S. Constitution implies this possibility), but not under state laws (the two are distinct due to the Supremacy Clause of the U.S. Constitution).

Some of the opinions of the U.S. Supreme Court in its recent decision this year on Presidential immunity from a subpoena imply that there is not immunity for prosecution for crimes committed by a President before taking office, although there might be strong grounds to defer a trial in most or all cases.

There might be some exceptions to this for violations of federal laws targeted at official capacity conduct (e.g. bribery, theft of government property, Posse Comitatus Act violations, etc.) if the prosecution is for official conduct after being removed from office.

The impeachment language of the U.S. Constitution implies that a President may be prosecuted for at least some crimes committed while in office, in Article I, Section 3 of the U.S. Constitution which states that:

Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.

But not under state laws (the state and federal cases are distinct due to the Supremacy Clause of the U.S. Constitution).

Some of the opinions of the U.S. Supreme Court in its recent decision this year in Trump v. Vance on Presidential immunity from a criminal subpoena imply that there is not immunity, at least, for prosecution for crimes committed by a President before taking office (necessary to avoid a statute of limitations issue, for example), although there might be strong grounds to defer a trial in most or all cases.

From the official syllabus of the case (citations omitted):

Here, the President claims that the Supremacy Clause gives a sitting President absolute immunity from state criminal subpoenas because compliancemwith such subpoenas would categorically impair the performance of his Article II functions. The Solicitor General, arguing on behalf of the United States, claims that a state grand jury subpoena for a sitting President’s personal records must, at the very least, meet a heightened standard of need.

The President’s unique duties as head of the Executive Branch come with protections that safeguard his ability to perform his vital functions. The Constitution also guarantees “the entire independence of the General Government from any control by the respective States.” Farmers and Mechanics Sav. Bank of Minneapolis v. Minnesota. Marshall’s ruling in Burr, entrenched by 200 years of practice and this Court’s decision in Nixon, confirms that federal criminal subpoenas do not “rise to the level of constitutionally forbidden impairment of the Executive’s ability to perform its constitutionally mandated functions.” Clinton v. Jones. But the President claims that state criminal subpoenas necessarily pose a unique threat of impairment and thus require absolute immunity. His categorical argument focuses on three burdens: diversion, stigma, and harassment.

The President contends that complying with state criminal subpoenas would necessarily distract the Chief Executive from his duties. He grounds that concern on Nixon v. Fitzgerald, which recognized a President’s “absolute immunity from damages liability predicated on his official acts.” But, contrary to the President’s suggestion, that case did not hold that distraction was sufficient to confer absolute immunity. Indeed, the Court expressly rejected immunity based on distraction alone 15 years later in Clinton v. Jones, when President Clinton sought absolute immunity from civil liability for private acts. As the Court explained, Fitzgerald’s “dominant concern” was not mere distraction but the distortion of the Executive’s “decisionmaking process.” The prospect that a President may become “preoccupied by pending litigation” did not ordinarily implicate constitutional concerns. Two centuries of experience likewise confirm that a properly tailored criminal subpoena will not normally hamper the performance of a President’s constitutional duties.

The President claims this case is different. He believes that he is under investigation and argues that the toll will necessarily be heavier in that circumstance. But the President is not seeking immunity from the diversion occasioned by the prospect of future criminal liability. He concedes that he may be investigated while in office. His objection is instead limited to the additional distraction caused by the subpoena itself. That argument, however, runs up against the 200 years of precedent establishing that Presidents, and their official communications, are subject to judicial process, see Burr, even when the President is under investigation, see Nixon, . . .

Finally, the President argues that subjecting Presidents to state criminal subpoenas will make them “easily identifiable target[s]” for harassment. Fitzgerald. The Court rejected a nearly identical argument in Clinton, concluding that the risk posed by harassing civil litigation was not “serious” because federal courts have the tools to deter and dismiss vexatious lawsuits.Harassing state criminal subpoenas could, under certain circumstances, threaten the independence or effectiveness of the Executive. But here again the law already seeks to protect against such abuse. First, grand juries are prohibited from engaging in “arbitrary fishing expeditions” or initiating investigations “out of malice or an intent to harass,” United States v. R. Enterprises, Inc., and federal courts may intervene in state proceedings that are motivated by or conducted in bad faith. Second, because the Supremacy Clause prohibits state judges and prosecutors from interfering with a President’s official duties, any effort to manipulate a President’s policy decisions or to retaliate against a President for official acts through issuance of a subpoena would be an unconstitutional attempt to “influence” a superior sovereign “exempt” from such obstacles, see McCulloch v. Maryland. And federal law allows a President to challenge any such allegedly unconstitutional influence in a federal forum.

A state grand jury subpoena seeking a President’s private papers need not satisfy a heightened need standard, for three reasons. First, although a President cannot be treated as an “ordinary individual” when executive communications are sought, Burr teaches that, with regard to private papers, a President stands in “nearly the same situation with any other individual.” Second, there has been no showing here that heightened protection against state subpoenas is necessary for the Executive to fulfill his Article II functions. Finally, absent a need to protect the Executive, the public interest in fair and effective law enforcement cuts in favor of comprehensive access to evidence. Rejecting a heightened need standard does not leave Presidents without recourse. A President may avail himself of the same protections available to every other citizen, including the right to challenge the subpoena on any grounds permitted by state law, which usually include bad faith and undue burden or breadth. When the President invokes such protections, “[t]he high respect that is owed to the office of the Chief Executive . . . should inform the conduct of the entire proceeding, including the timing and scope of discovery.” Clinton. In addition, a President can raise subpoena-specific constitutional challenges in either a state or a federal forum. As noted above, he can challenge the subpoena as an attempt to influence the performance of his official duties, in violation of the Supremacy Clause. And he can argue that compliance with a particular subpoena would impede his constitutional duties.