Does gun control reduce violent crime?
For a few policies, probably yes. Otherwise the research is inconclusive.
RAND Corporation conducted a comprehensive review of studies on gun policy, considering 18 gun policies which are sometimes implemented in America. Criminological research may be suffering from a hidden replication crisis, but RAND researchers at least excluded low quality studies as well as they could. For 11 gun policies, no good evidence was available to say whether the policies affected violent crime. For 6 gun policies, there was "limited" or "moderate" evidence that restrictive measures reduced violent crime, meaning RAND found one or some studies which supported gun control claims but the studies were still somewhat weak and debatable. Only for a single policy was there "supportive" evidence that restrictive gun policy reduced violent crime; specifically, repealing stand-your-ground laws was expected to reduce violent crime.
Commentary published by the National Firearm Industry Trade Association and National Review argued that RAND's review, while fairly good, did overstate the amount of evidence supporting several types of gun restrictions.
The libertarian outlet Reason criticized RAND's analysis and argued that research on gun policy yields no sound conclusions whatsoever, but its criticisms were mistaken.
Ultimately, there is decent evidence that repealing stand-your-ground laws, passing waiting period laws, and passing stricter laws keeping guns out of domestic violence situations would reduce violent crime. On other subjects, the situation varies from weak evidence in favor of gun control, to no good evidence either way.