Washington (CNN) President Donald Trump has made a blizzard of claims about Ukraine, China and the impeachment inquiry. Many of them have been attacks on Democrats, and many of them have been incorrect.

Here is a brief readers' guide to our fact checks on all things related to Trump's Ukraine controversy and the resulting impeachment inquiry.

This post will be updated as events unfold.

Hunter Biden and the investigation

Trump has repeatedly claimed that former vice president Joe Biden had called for the firing of a Ukrainian prosecutor who was "investigating his son." There is no evidence Hunter Biden was ever under investigation. The investigation was into the business dealings of the owner of a Ukrainian natural gas company, Burisma Holdings, where Hunter Biden sat on the board of directors. In addition, a former Ukrainian deputy prosecutor and top anti-corruption activist have said the investigation was dormant at the time. And chief prosecutor Viktor Shokin's successor, Yuriy Lutsenko, has said in interviews this year that Hunter Biden didn't violate any Ukrainian laws.

Full fact check here

Joe Biden's pressure on Ukraine

Trump has also claimed that Biden pressured Ukraine to take chief prosecutor Viktor Shokin "off the case." Biden pressured Ukrainian leaders to fire Shokin -- the Obama administration, US allies and Ukrainian anti-corruption activists saw Shokin as unwilling to prosecute elite corruption -- but there is no public evidence that Biden sought to get Shokin removed from any particular case.

Full fact check here

Joe Biden's boasting

Trump claimed in his July phone call with Ukrainian President Volodymyr Zelensky that Biden had boasted about having "stopped the prosecution." Biden had boasted about getting Shokin fired, but he did not say he had stopped any prosecution. Shokin had been controversial precisely because he was unwilling to bring corruption prosecutions.

Full fact check here

The Bidens and China

Trump has claimed that "Joe Biden and his son walk(ed) away with millions of dollars from Ukraine and then millions of dollars from China." There is no basis for Trump's claim about Joe Biden. A company on whose board Hunter Biden sat, however, received a large investment of Chinese capital shortly after Hunter Biden visited the country with his father, and Hunter Biden later purchased an equity stake in the company. A lawyer for Hunter Biden says he has not received any return or compensation from his investment or board position.

Full fact check here

Trump has also conflated Hunter Biden's involvement in Ukraine and China. On October 4, after speaking to reporters about Biden and China, Trump said, "Now I'm hearing the number $50,000 a month." That is the approximate amount the New York Times has reported Biden was paid for his board role with Ukrainian company Burisma, not an amount related to China. Trump then claimed, seconds later, that Biden was "getting hundreds of thousands a month," a number for which there is no public evidence.

Joe Biden's previous comments

Trump said Joe Biden contradicted himself when he said in September that he had "never" spoken to his son Hunter about his son's overseas business dealings; Trump claimed Joe Biden had previously said the opposite. That is not true. Hunter Biden, however, did tell the New Yorker that there was one father-son conversation about his business dealings in Ukraine.

Full fact check here

The delay in aid to Ukraine

Before he began justifying his decision to delay military aid to Ukraine, Trump told reporters that there was no delay at all -- an assertion obviously contradicted by the facts.

Trump suggested on September 23 that he froze the funds because he was worried about "corruption" and whether "that country is honest." He explicitly said on September 24 that the funds were withheld, this time claiming he was waiting for "Europe and other nations" to spend their own money on Ukraine.

A full fact check is here

European aid to Ukraine

Trump has repeatedly claimed the US is the "only" country providing aid to Ukraine, and he has specifically accused certain European countries of doing nothing. In reality, the EU has sent several billion dollars to Ukraine over the past few years.

Full fact check here

Obama's aid to Ukraine

Trump suggested that Barack Obama sent only "pillows and sheets" to Ukraine, not the lethal arms he has himself sent. This was hyperbole. While Trump is correct that Obama refused to provide lethal assistance, Obama did provide armored Humvees, drones, counter-mortar radar, night vision gear and medical supplies.

Full fact check here

CrowdStrike

In his July phone call with Zelensky, Trump made vague claims about CrowdStrike -- the American cybersecurity company he has wrongly described as Ukrainian -- and "the server." These claims were confusing, but we tried to explain what he might be talking about:

In short, Trump seemed to be alluding to a baseless conspiracy theory that Russia was not responsible for hacking Democratic National Committee computer servers during the 2016 election. CrowdStrike, hired by the DNC to investigate the hack, had said Russia was responsible, a finding later corroborated by special counsel Robert Mueller.

Trump's personal lawyer Rudy Giuliani has been among the people pushing a theory that Ukraine interfered in the 2016 election through "collusion" with Democrats.

Full fact check here

The Democrats' letter to Ukraine

Trump claimed that a 2018 letter from three Democratic senators to Ukraine's prosecutor general made a threat to withdraw US assistance if Ukraine did not do what they wanted. The letter did not make a threat; it urged the prosecutor not to close investigations into former Trump campaign chairman Paul Manafort or stop cooperating with Mueller to avoid angering Trump, as the New York Times reported had happened.

Full fact check here

Schiff's comments

Trump criticized Democratic Rep. Adam Schiff for Schiff's comments at a House Intelligence Committee hearing with the acting DNI. In a tweet, he said Schiff's remarks were made "illegally." It is very much not illegal to do a bad paraphrase in a congressional committee meeting. The Constitution has a specific clause that lets legislators say what they want during congressional business without facing legal repercussions.

Full fact check here

Treason

Trump called Schiff's rendition of Trump's July phone call with the President of Ukraine "treasonous" in an exchange with reporters alongside the Finnish president.

None of this is anything close to "treason," a word with an actual, narrow definition in the Constitution.

Full fact check here

The whistleblower

Trump said the whistleblower's account of his call with Zelensky was "totally wrong." The whistleblower's three chief allegations were all correct.

Full fact check here

Whistleblower complaint

In response to a New York Times report that Schiff knew about the whistleblower's concerns before the official complaint was filed, Trump claimed that Schiff "knew long before and helped write it, too."

Spokespeople for both Schiff and the whistleblower denied the allegations.

Full fact check here

An 'exact transcript'

Trump claimed that the document released by the White House is an "exact transcript" of his call with Zelensky.

It is not an exact transcript. We know this because the document itself says so.

Full fact check here

The whistleblower complaint form

Trump tweeted out a conspiracy theory that the form to submit whistleblower complaints was secretly changed to allow those with secondhand information to submit complaints.

There have been no changes to the rules surrounding who can submit a whistleblower complaint.