This bears some confusion. Gerrymandering is a real thing, but it is not the primary problem with (from the other answer)
Regardless of which side is doing it, a portion of the population is not getting a fair representation and that's (again in my opinion) a problem.
The number one reason why people lack representation in the United States is always going to be the winner-take-all system. Each congressional district elects one Representative, and those who did not vote for that candidate do not get representation of their choice. This disenfranchises up to half of the population in each district. I.e. urban Republicans and rural Democrats do not get representation.
The efficiency gap is looked at on a group basis, mostly per state because that is where redistricting occurs. It measures how many votes are wasted or lost because they either take the vote above 50% for the winner or are votes for the loser. So there will be an efficiency loss of 50% for every district, split between the two parties (efficiency gap analysis ignores others).
At the national level it could be argued that the gerrymandering might be even itself out to some degree (not sure if that's the case or not - from the numbers I've seen it appears that the GOP has an advantage) but in my opinion two wrongs don't make a right.
Efficiency gap analysis doesn't measure that. In fact, it does the exact opposite. It says that if one side is benefiting more than the other side, that we should transfer some of that benefit to the other side. This doesn't change the amount of disenfranchisement. It just moves it from one side to the other. Because that eliminates the gap in the efficiency. I.e. it is all about making the wrongs even. It makes no attempt whatsoever to remove the wrongs.
Worse, efficiency gap analysis encourages the introduction of wrongs. Normal redistricting might put an entire county in the same district while efficiency gap analysis encourages breaking up cities and counties to produce "fairer" districts.
From a comment:
Democratic votes being concentrated in cities doesn't matter for gerrymandering. It isn't a problem to have a lot of geographically small districts inside a city, while having a small number of very geographically large districts in rural areas. In other words, you can make the districts "fair" even given the demographics.
The normal problem with urban vs. rural districts for gerrymandering is that urban districts are more Democrat (have a higher efficiency loss for one party) than rural districts are Republican. This is why efficiency gap analysis is promoted by Democrats as a measure of gerrymandering. It promotes their goals of more Democratic districts with very little loss of districts to the Republicans.
Look at states like Massachusetts and Connecticut for example. In both states, the congressional delegation is entirely Democratic. But in both states there is a large enough Republican minority that they occasionally win the governorship. In Massachusetts, the breakdown is roughly 50% Democrat, 25% Republican, and 25% other. So in a proportional system, the Democrats should have four to five seats while the Republicans and other each have two to three seats. As is, Republicans and other have zero seats. In fact, nationally, other has zero seats in the House of Representatives.
Efficiency gap analysis doesn't help with that. In fact, in a state with 75% or more of voters in one party, efficiency gap analysis says that the majority party should get 100% of the seats. The disenfranchised 25%? Not their problem. Same thing with those not in the two major parties.
Source: Partisan Gerrymandering and the Efficiency Gap (PDF), Nicholas 0. Stephanopoulos & Eric M. McGhee
Election analyst Sean Trende of Real Clear Politics did an analysis of gerrymandering where he measured the increase in partisanship. He found
If we define “Highly Partisan Districts” as those that are four points or more Republican (or Democratic) than the country as a whole, there were 195 such districts in 2010, and 200 in 2012. In 2000, under the previous set of lines, there were 193 “highly partisan” Republican districts.
So Republicans added five "Highly Partisan Districts" during the redistricting cycle of 2010-2012. And seven if we count from 2000 (which includes two redistricting cycles. This is noteworthy because prior to that, it was Democrats who controlled redistricting in most states. It's only the last couple censuses where Republicans have been able to gerrymander more than Democrats.
The Washington Post Redistricting Scorecard used to show the same five seat advantage for Republicans in the last redistricting.
It's worth noting that both of these include North Carolina. Why is that important? Democrats controlled the state legislature and governorship in North Carolina in 2001 when the last redistricting had been done. And they gerrymandered the heck out of it. So about half the gains in North Carolina in 2012 were not from the introduction of a Republican gerrymander but from the elimination of the Democratic gerrymander.
Fair Vote analyzed the North Carolina districts. They have a plan to combine districts into superdistricts with three to five seats in each. Under that analysis, they found that North Carolina should have a slight Republican lead but that Democrats should be able to win 7-6 in a good year while Republicans could win up to 8-5. The average result would be a 7-6 victory for the Republicans.
Note that the actual results swung from 8-5 Democrat to 10-3 Republican. This accounts for the entire improvement from 2010 to 2012 among Republicans, all five seats. Yet half of this was the elimination of the previous Democratic gerrymander. If we knock off two seats, the Republicans would have only gained by three seats by gerrymander. The other two being gained from the elimination of a gerrymander.
An analysis on Politics.SE found that under Cook Partisan Voting Index, Republicans did better than their national average in just three more districts in 2008/2012 versus 2004/2008.
TL;DR: Republicans gained three to five seats in the 2011 redistricting. depending on how one measures.