We've learned a lot more about the Bidens since this question was first posted. Let me start by saying that US law does not prevent anyone except a public official's spouse from accepting money from foreign governments so technically, Hunter Biden (Joe's son) is in the clear. He hasn't committed a crime. On the surface, Joe Biden is also in the clear. The fact is that while Joe was the VP of the US in charge of Ukraine oil policy (and the money that went with it) and his son took a "no show" job with the most corrupt oil company in the Ukraine that paid him and his business partner each a million dollars a year simply doesn't pass the smell test. What justified the generous payments to Hunter? He had no knowledge of the oil industry, he didn't speak Ukrainian, and yet he was being paid far more than would be considered normal in the US for board members. While the situation smells, it is quite a reach to prove that Joe was giving the Ukraine special treatment in exchange for the "no show" job for his son. There are certainly obviously favorable decisions but proving quid pro quo is very difficult. At the time (2016), some newspapers investigated the story and John Kerry's (secretary of state) stepson who was also a business partner of Hunter and the third guy complained to federal authorities about the relationship and distanced himself from his two former partners who he felt were cashing in on the Biden name and that the arrangement was corrupt (his own words). Then the matter was dropped. Did someone in the Obama administration tell the press to drop the investigation? We'll never know. What we do know is that the press is completely in the tank for the Democrats and bringing this to the front page would embarrass the Bidens at best and at worst subject them to charges of corruption.
Then the worm turned because Joe, himself, couldn't keep his mouth shut. Sometime last year, Joe was speaking to a group of donors and the speech was recorded and leaked. So, Joe was bragging to the donors about how he threatened the Ukraine president with withholding 1.5 billion dollars of US loan guarantees if he didn't fire the prosecutor who was investigating corruption at Burisma which was the corrupt oil company that his son Hunter had the "no show" job with. THIS is the crime. THIS is the quid pro quo and Joe did it to himself and the Democrats refuse to even consider that this might be a problem that Joe was using his power to influence a foreign government and was directly benefiting his son by the action.
One of Trump's campaign promises was to clean up the "swamp". This is why the Republicans hate him as much as the Democrats. The Republicans are a little more subtle in their corruption but people who get elected to the Senate and the House and manage to stay for a few terms somehow become millionaires (Nancy Pelosi uses her position to funnel contracts to her husband's business). We pay them too well (~$180,000) but given the expense of having to maintain two residences, it is not that outrageous. To ensure their success, congress has passed laws that exempt themselves and their staffs from insider trading laws so given that they know ahead of time which way the wind is blowing, they can take advantage of that knowledge to control their investments. This was reported a few years ago on a 60 minutes segment prompting a change in the law. The change lasted a few months and it was quietly modified again and they are back to their old tricks.
Anyway, back to Trump. In July (?) he had a phone call with the new President of the Ukraine and as part of the conversation asked the president to do "US" a favor. Not "ME", "US" and look into some of the corruption that was being reported. Although recordings are not made of these calls, numerous people are listening in and making notes about what transpired so there is a "transcript" which Trump released as soon as the Ukraine president agreed.. One of the people on the call misinterpreted Trump's request and thought Trump was asking for dirt on Joe Biden so he could use it to defeat Joe in the upcoming election and this was the final nail that motivated the Dems to start to impeach Trump. The groundwork for the impeachment had actually been laid during the Obama administration when the FBI lied to the FISA court and got authorization to spy on the Trump campaign. Trump wasn't delusional when he was talking about phones at Trump Towers being tapped although it wasn't quite as direct as that. This spying ultimately led to the Mueller special prosecutor investigation which led to nothing nor did any of the other investigations conducted by the House. Trump came out essentially clean or at least as clean as someone as flamboyant and hated as Trump could. So, that left the "call" as the Dem's last best hope. Sadly, Trump haters are completely blinded by the defamation campaign that has been going on since he beat Hillary so they don't remember that Democrats actually started calling for Trump's impeachment 19 minutes after he took the oath of office. They hated him with a purple passion and nothing, nothing was ever going to convince them that he didn't cheat and steal the election from Hillary.
Nothing in the impeachment or other investigations has turned up a crime. All we have are a president exercising his prerogatives as President. The opposition witnesses testified basically that they disagreed with Trump's actions but when asked, not a single one of them could cite a crime. This didn't stop the Dems. They edited the depositions and only showed the parts where the witnesses were talking about how bad the President's decisions were and how he was ignoring all their advice and just doing whatever he wanted. Of course, the Constitution specifically gives the President the sole power to conduct foreign policy. We don't conduct foreign policy by committee, The state department staffers are not elected. They don't get to decide policy. It is their job to implement the President's policy and if they don't want to, they need to quit. Instead, they stay and obstruct and leak and do what ever they can to disrupt his plans. The President has 100% complete discretion on who we will be friends with. Who we will make treaties with (the Senate must ratify treaties but they don't make them), etc.
Trump is his own worst enemy. He's a ham. He makes jokes that are always misinterpreted. The one about asking Russia to get Hillary's emails is a prime example. Do people really think that he is stupid enough to ask the Russians for help on national television? I know Obama did but Obama didn't know the mic was live. Trump spent too many years as a man about town in Manhattan and later on the reality show the Apprentice. He offends people and he often does it deliberately because he loves to watch their heads spin. Smoke comes out of their ears and they call him insane because they simply cannot comprehend what he is all about. At his heart, Trump is a successful businessman (probably not as successful as he'd like us to believe. He's bigger than life. He exaggerates.). He's used to telling people what to do and having them do it. If a plan doesn't produce the desired results, he changes the plan and tries something else. For this they call him erratic. Apparently, once the lemmings are headed for the cliff, there is no getting out of line even if you happen to be tall enough to see the precipice. You just have to keep going. Maybe nothing bad will happen. He went to military school as a boy. He studied Machiavelli and Sun Tzu. He took to heart the concept of keeping your friends close but your enemies closer. To me, as I watch him suck up to some dictator, I wonder why the dictator buys it, not why Trump does it. He does it because it works. It gets them to talk to us and come to the bargaining tables. If it weren't for the damn press undermining him at every opportunity, North Korea would have disarmed by now and would be welcoming US businesses into the newest far east cheap labor market.