Gerrymandering is a problem; a Representative could have their voter base diluted across neighboring districts at the whim of the controlling party. But Senate elections are statewide, and states don't tend to change shape a lot. Given that Senators are elected by popular vote, does this mean that gerrymandering has no direct effect on the election of US Senators?
Yes. Currently gerrymandering has no effect on US Senators.
However, before the ratification of the 17th amendment to Constitution, Senators were elected/chosen by the state legislature. The state legislature, including its senators(at least in my state), have and have had districts. So, since gerrymandering started "officially" in 1812 and since the 17th amendment wasn't passed for another 100 years, US senator elections could have and probably were affected by gerrymandering. Although, its effect was more indirect.
While the state-wide nature of gerrymandering would make one think that it has no effect, it certainly could.
Elections are run at the state level, so a state-gerrymandered election could alter that balance of power in the state legislature, which would effect things like voter-suppression measures, enactment and enforcement of campaign finance regulations, and the ability of elections to be monitored and for rules to be enforced by non-partisan (or partisan) entities.
In Wisconsin, this was, in part, the basis of their gerrymandering case/challenge that will now be heard by the Supreme Court. In 2012, Democratic candidates got the majority of State Assembly votes, but the GOP won a huge majority in that lawmaking body. The GOP enacted voter ID and other restrictive measures, that have been struck down, then reinstated, by different levels of the courts.
It would be difficult to claim this did not have an impact on state-wide results. Those in power (regardless of party) tend to favor policies and practices that perpetuate their power.
The above examples are correct that current gerrymandering does not have an effect on US Senators.
However, the division of territory into states itself has been alleged to be a consequence of gerrymandering, specifically in the late 19th Century the Republican party ensured that more states were created in territories friendly to their party, notable Dakota being admitted as two states and not as one.
The idea of gerrymandering is that you draw districts to give your party an advantage. Like if there are 100,000 Party A voters and 100,000 Party B voters to be divided among 10 districts, a fair election should presumably result in 5 winners for party A and 5 for party B.
But suppose the people with the authority to draw district lines prefer party A. Even if they are obligated to make every district have the same number of voters, they could, at the most extreme, draw 1 district that has 20,000 B's and 9 districts each with 8,889 B's and 11,111 A's. Then they end up with A winning 9 seats and B winning only 1.
But you can't do this for Senate elections, because Senators don't have a district, they represent the entire state, and state boundaries are essentially fixed. I suppose when the state borders were originally drawn Congress may have tried to do some gerrymandering, but any such effort would have only short-term value as people move and political opinions change. As it's now been almost 60 years since the last state entered the union, it's unlikely that any attempts to gerrymander back then would still have the expected results. State borders change occasionally, but those are minor adjustments. I don't know what the most people ever moved to another state through such an adjustment is. Maybe somewhere along the line there was an election that was close enough and enough people moved that it changed the outcome.
I suppose that, as @PoloHoleSet says, gerrymandering could have indirect results. A change to the composition of the state legislature could lead to different election laws which could change the outcome of a Senate race.
I agree with PoloHoleSet that there could be important indirect effects of gerrymandering. He mentioned voter suppression, which is certainly a problem in my state of North Carolina. Gerrymandering could also affect voter turnout, especially in off-year elections. For example, I live in a heavily Democratic county, so Democratic that we can swing statewide elections. In an off-year, voters know our Congressional and state reps are going to be Democratic, so local voters might not be as motivated to take the time to go the polls. If there happens to be a Senatorial election, those are votes left on the table for the Democratic candidate.
In addition to what every body else said (and excellent answers) it also depends on your exact definition of gerrymandering.
Besides the intentional gerrymandering, there also is unintentional gerrymandering. Some people argue that this might actually be a bigger problem than the intentional gerrymandering - one example is white flight, which in effect resulted in de-facto gerrymandering between downtowns and suburbs, even without redrawing districts.
This type of unintentional gerrymandering does take place on a massive scale on the state level, as well. One example where this was particularly obvious was the 2016 Presidential election, where one candidate won one large state by such a massive margin, and lost many smaller states by slivers of margins, that one single state by itself caused the electoral college result to differ from the popular vote (the state was California - if add up the remaining 49 states and DC, the other candidate comfortably won the popular vote as well as the electoral college). That is, of course, the classic effect how gerrymanders work. Of course, she also won a few other states, some by large margins, but the margin in California was higher than the nationwide margin.
Another example of (intentional) state-level gerrymandering is the "Free State Project", which aims to recruit 20,000 libertarian volunteers to move to a low-population state (they selected New Hampshire) in order to "take over" that state.