I haven't said much about the impeachment process, because there hasn't been much to say. Impeachment itself is just bringing charges; the charges that were eventually made were, I'm very sure, much more vague and less serious than Democrats were hoping. In principle, of course, since the point of impeachment is to give primacy to the legislature, the House can impeach any civil officer of the United States for anything whatsoever that it regards as misconduct; it is the sole authority on what counts as 'high crimes and misdemeanors', and the power has never been understood to require a legally defined crime at all. (In the first impeachment that went to conviction, that of John Pickering, it was universally recognized that there was no crime committed in a strict sense; Pickering was removed because he was a mentally ill alcoholic and was becoming increasingly erratic. Usually when an impeached official is convicted and removed, a criminal trial is held for the offenses, but nobody even tried to indict Pickering on anything. As a side note, one of the 'high misdemeanors' in his impeachment was that he was making a bad example because, when drunk, he swore, profaning the divine name in public.) In practice, it really needs to establish that something identifiable as a crime in at least a broad and loose sense has been committed. The charges against President Trump are 'abuse of power' and 'obstruction of Congress', which are about as broad and loose as you can get.
Some people have warned that this could set a precedent for attempting to impeach every President, but in fact we already live in this regime: Clinton was impeached; attempts to impeach both Bush and Obama were begun but petered out due to lack of political will and opportunity; Trump has been impeached.
Everything goes to trial in the Senate now, which alone has the power to remove a President from office; at least one of the two charges will require a guilty vote from at least two-thirds of the Senate for anything to come of it. In principle, if it convicts, the Senate can also disqualify the person in question from future office, but this is a hard sell even in very obvious cases. The Senate is the sole authority in such trials; famously, in the very first, that of Senator William Blount, the Senate opened its trial and then voted that the House of Representatives had no authority to impeach a Senator. (The Senate instead removed him by its own power to expel Senators.) This is why you find Democrats voicing the absurdity of not transmitting the articles of impeachment to the Senate; the Senate is not expected to push for conviction, and the Senate can pretty much do whatever it wants in the matter. To be wholly honest, I think it's a pointless game; the Senate explicitly has the power to try all impeachments, so if the House has impeached, the Senate could very well try it if it wanted, although there's no precedent for how to do that. Everything else is legislative courtesy. But if the House doesn't transmit, the Senate will likely just go on as it has been, as if there were no impeachment at all. A bizarre situation, but we seem to be in a snowstorm of bizarre situations.