Not much to be perfectly honest.
For all of the talk of a "Blue Wave" cresting over Texas, which didn't happen, I think it's pretty safe to say that the County of Harris has flipped almost completely Blue and it's not close.
Consider:
Straight party voting:
Republicans: 408,413 44.12%
Democrats: 511,282 55.24%
Libertarian: 5,935 00.64%
All local Republican judges were voted out of office.
Harris County Elected officials:
County Judge:
Ed Emmett (R - I) 572,816 48.23%
Lina Hildago (D) 590,524 49.72%
Eric Gatlin (L) 24,379 2.05%
District Clerk:
Chris Daniel (R - I) 529,658 44.97%
Marilyn Burgess (D) 648,097 55.03%
County Clerk:
Stan Stanart (R - I) 507,394 42.92%
Diane Trautman (D) 644,792 54.54%
Abel Chino Gomez (L) 30,127 2.55%
County Treasurer:
Orlando Sanchez (R - I) 540,880 45.85%
Dylan Osborne (D) 638,825 54.15%
As you can see from the above the defeat was all-encompassing, and total. All that the Harris County GOP has left in the fold is Texas State Senate District 7 (Paul Bettencourt won with 57.83% of the vote) and some Texas house districts either wholly or partially contained in that geographical area. US-TX 2 (Won by Dan Crenshaw with around 53% of the vote, has a large part of it's geography contained within, as does US-TX 7 (Won by Fletcher (D) over Culberson (R - I) 52.35% - 47.65%) but not enough to pull Culberson through. There was good news in US - TX 10, where Mike McCaul won re-election with 62.69% of the Harris County vote (the final result in the race though was much closer), but in the statewide races it was even worse....
"Beto" O'Rourke beat Ted Cruz in Harris County by a full 16 points.
No Republican state-wide candidate won Harris County in a race where they were opposed by a Democrat.
The highest Republican vote-getter, by percentage, was Greg Abbott at 46.47% and he was running against someone who couldn't pay their taxes on time.
Despite (or perhaps because of) a slew of robo-calls (I received NINE on Monday evening before the election), scary mailers about an invasion that was coming and how everyone was going to be forced to house violent immigrants and judges releasing dangerous criminals into the population, Harris County voters just said no.
The easy answer for this, for the angry Republican set, is that the "Gimme" voters (everyone but them) voted for the party that promised to give them more. The harder answer is that the current Harris County GOP is a county party bereft of ideas, leadership, and any sense of a vision for the region that doesn't involve cutting taxes or turning the Astrodome into a high-priced parking garage.
I can't imagine that any of the current officers of the HCGOP get to hang around after this shellacking, but you'd be surprised what the crony system can produce. There is a way Paul Simpson could survive, by (incorrectly) blaming the evil mainstream media and "Betomania" he might just convince enough people that he's the guy to lead them out of the wilderness.
Of course, he's still going to have the problem of all of the pay-to-play slates sending out what basically amounts to scare-mongering and (in some cases) hate-mail to voters, and then there's the issue that on almost none of the local issues does the HCGOP seem to have much of a platform that people understand.
I believe that there are good, conservative policies that urban voters might gravitate toward as they start to understand the blight that is big-government cronyism and the damaging effects it can have on communities. At the local level especially conservatives should have a laser-like focus on infrastructure (including flood control) better schools (which can include school-choice) through a plan that doesn't involve gutting the public school system and government transparency.
What people WANT from a local government are roads that work, traffic that flows, safe neighborhoods and a government that's not working against them and then trying to cover it up.
I don't see a Harris County Republican Party that's really all that focused on that right now.
Which is why they lost. Not because some greedy people just had their hand out. That excuse is too easy and should be immediately discarded.
It's either that or be ready for one-party rule in Harris County for a long, long time.