Bleach is a very effective mold killer, killing something like 99.9% of mold. For comparison, vinegar kills about 82% of molds. Hydrogen peroxide (H2O2) is a decent biocide, but not notably more effective than bleach. It is generally not effective in concentrations less than 10%. The stuff you get at the ********* is typically 3%, which won't do much. You can buy 35% H2O2 if you look around - it's expensive. I have some right now that I mixed down to 10%... a quart cost $30. In the concentrations needed to kill mold effectively, H202 is dangerous to handle. It can cause permanent eye damage, as well as skin burns. And, it quickly breaks down into water and oxygen. I don't hink it worked any better than Clorox, it just cost more and was more dangerous to use.
On the other hand, bleach is a few bucks for a gallon, and you probably already have some in your laundry room (but you SHOULD use fresh bleach for mold work). Most sources recommend no more than one cup of unscented bleach per gallon of water. Some recommend stronger bleach solutions, but once the mold is dead, it's dead. There's little value in super strong solutions. Bleach is recommended for mold remediation by a number of state health agencies, and is mentioned by the EPA (more on this later) but not recommended (nor is any biocidal agent) for mold remediation work.
I believe that boric acid is a good material to use. Its main advantage is it is stable - doesn't break down easily - and thus may retard the growth of mold for a good long time. I mix up a solution of boric acid and water and spray it on the studs, subfloor, etc AFTER the bleach has been applied and allowed to dry thoroughly. I don't advise mixing chems of any type. Some mixtures may be dangerous, others may simply react in such a way that they don't work at all.
The EPA, contrary to a lot of the info on the internet, has never said that bleach is ineffective. What they HAVE said is that in general, it is ineffective and unnecessary to use ANY biocide to remediate mold. Basically, it is a losing battle. Mold is everywhere in our environment, like bacteria. The spores are present in the lumber RIGHT FROM THE MILL. We've all seen green doug fir at Home Depot that are stained black right on the pallet. That's MOLD... and yes, many mills apply biocides at the mill to retard the growth since people generally don't want to buy wood that has mold on it! But I digress. The EPA says that the best approach is to forego the killing and just remove the mold by vigorous scrubbing with detergent! This is very hard and nasty work. But even if you do try to kill the mold, you STILL have to scrub! Some materials such as drywall and (most of the time) carpeting are best replaced. If all the mold is removed and the moisture problem is solved, the mold should go dormant and not grow.
Other (state) agencies do recommend biocides for mold remediation. Bleach solutions are most often cited.
There is a lot of misinformation on the internet about bleach. Almost all of it comes from people that are selling other mold killing chemicals, including 35% H2O2 and boric acid -- usually at insanely high prices.
Whether you choose to apply a biocide or simply remove the mold by scrubbing with detergent, it IS critically important to remove the mold. The allergens and toxins in mold are present whether is dead or alive... so you need to get rid of it. It is generally a good idea to never try to remove dry mold. Wet it first! This helps keep the allergens and toxins and spores from becoming airborne and getting all over - and into - other things. Like your lungs or eyes, or the rest of your home.
I've used bleach, vinegar, peroxide and boric acid. Here's what I think is the best approach - but be forewarned this is MY OPINION ONLY - you are responsible for your own actions so learn about this and reach your own conclusions. If you don't want to do this, hire a professional mold remediation firm. The following is simply what I choose to do, it is not a recommendation or advice. First, I seal off the area with 6 mil plastic, 100% taped at the edges. I use an appropriate respirator, as well as gloves, eye protection. I have a forced air system that I use for painting cars which comes in handy and protects lungs and eyes, but is probably overkill. I have also used a NIOSH N-95 mask. I then wet the infected area with a solution of one cup of unscented 6% sodium hypochlorite bleach per gallon of water. I next remove as much of the now-damp infected building material as possible, keeping it all wat to keep the dust (and spores) down. When in dount, I tent to tear it out. Some say you can save carpet. I don't try. I also discard drywall and any nasty looking wood framing (I'm careful to decide of it's load bearing structure and if it is, deal with it appropriately). I scrub for a couple of feet (at least 2 and often more) past the problem -- into walls and floor that show no evidence of mold. Once the bulk of the infection is removed, I scrub the remaining mold off with a mixture of automatic dishwashing detergent (containing you-guessed-it, bleach) and stiff brushes including steel wire brushes. After I get it clean, I let the area dry out thoroughly and look for any signs of mold that I missed. If I find some, I get rid of them with more bleach and scrubbing. The area has to be squeaky clean. The I replace any damaged vapor barrier, studs, subfloor, etc. and make 110% sure that the moisture problem that led to the mold has been completely resolved. After it's all very thoroughly dry, I mix up some more bleach (one cup per gallon of water) and spray it on with a spray bottle (small area) or pump sprayer (large) -- just to get any mold on the surface that has survived undetected. Then I let this dry for a day or two. Next, I mix one cup of boric acid ( I get 99% boric acid marketed as ant and roach killer for $4-5 at Lowe's) with a gallon of water and spray that on. After THAT dries, I go ahead and put up the sheetrock, new flooring or whatever.
Needless to say, I hope.... I allow no pets or kids in the area until all this is done, dried and I'm satisfied that all is clean.
This has worked for me. There is a company called Foster that makes a line of special coatings that encapsulate and kill mold, and I will try these out next time on cleaned wood framing. I haven't had any problems without the Foster material... but belt and suspenders are a good idea when it comes to mold. These problems cause a lot of work and expense to repair.