The majority of studies either compare two different kinds of masks to each other, in a hospital setting, which is interesting but not the main thing we want, which is a comparison between mask and no mask. There are also a few studies looking at households where the housemates of a person with influenza-like illness are randomly assigned to use masks (or not); these studies find masks are not effective, but also show low compliance. In a household setting, most of the variance in whether a household member gets infected is likely explained by vaccination, other sources of prior immunity, and kitchen hygiene; whereas when considering infections of coronavirus occurring in public, none of these are factors. All studies had problems with noncompliance, and confounding between compliance and other precautions (ie people who comply with masks wash their hands at rates.)

This study is interesting in that it effectively has a "placebo mask" arm. There were three arms: a no-intervention arm in which health care workers continued wearing whatever masks they did before (less often than in either intervention arm, but still a significant amount), an intervention arm where hospital workers are given reusable cloth masks which do not work, and an intervention arm in which they're given disposable medical masks. The disposable medical mask arm did best, the cloth-mask arm did worst (worse than the no-intervention arm, due to a combination of not using other masks and taking fewer non-mask precautions). Presumably, this was able to get past an IRB because the study authors didn't know how bad cloth masks are.

Compliance (defined as "mask wearing more than 70% of working hours") was 57% in both the cloth mask and medical groups, and 24% in the no-intervention group.

The majority of infections in the study were from rhinovirus, which is transmitted via aerosol and contact droplets. These are the same modes of transmission as SARS-CoV2, but in different proportions; rhinovirus causes sneezing, so it generates a lot of aerosol, whereas SARS-CoV2 doesn't and aerosol is believed to be responsible for only a small portion of its transmissions. Other diagnosed infections in the study were from hMPV and influenza B. Rhinovirus has a smaller diameter than SARS-CoV2 (30nm), so it's unlikely that mask aerosol penetration of rhinovirus is higher than that of SARS-CoV2. In particle penetration tests, the cloth masks were almost completely ineffective, and the medical masks had some effectiveness but much less than N95.

Compared to cloth masks, medical masks reduced clinical respiratory illness from 7.6 to 4.8%, laboratory-confirmed viral infection from 5.4 to 3.3%, and influenza-like illness from 2.3 to 0.2%.

Scott Alexander has done a literature review called Face Masks: Much More Than You Wanted To Know. 

(If someone wrote an answer briefly summarising his conclusions and main evidences in 2-3 paragraphs, that would be a much better answer than this one.)

Some comments from Tara Mac Aulay on masks, in the context of donating to hospitals: 

Cross posting my comment from elsewhere re certification standards - KN95 is not sufficient in many settings, but still useful in some. Alibaba has a lot of masks available that are unsuitable, and not many masks that are. Finding the masks that are suitable and checking if the factory has been certified under the right standards is very useful

Alibaba suppliers commonly have KN95 masks in stock, but not surgical N95 masks.

In this time of shortage, many hospitals or healthcare workers will take what they can get, but there are some serious differences.

My understanding as is follows:

KN95 masks are tested for particle filtration to a similar standard as NIOSH rated N95 masks in the US. Surigical rated N95 masks certified by NIOSH have to pass a fit test and a fluid test in addition to the filtration tests standard for N95.

KN95 masks are not rated for use in many patient contact settings, they are predominantly designed for industrial use. KN95 masks provide limited protection to the wearer in this clinical setting, some versions also provide limited protection to patients.

In addition to passing the filtration tests, masks suitable for healthcare workers to use during Covid-19 care have additional requirements:

- masks that have a valve are not appropriate for treating suspected cases. Wearing a mask with a valve is much more comfortable, as the valve allows exhaled air to escape without restriction, meaning less force is required to exhale. However, masks with a valve do not protect patients from exposure from HCWs who are potentially infected. Thus masks with a valve should only be used with patients who are confirmed infected, and for some non-clinical staff who have had limited exposure. A mask with a valve is more comfortable for the general population, you'll be able to wear it for longer, and if you're mostly trying to protect yourself rather than others, this is ok. In some clinical settings, a mask with a valve is also ok. If you are buying masks for personal use to *prevent* yourself from becoming sick, get a mask with a valve. If you want to protect others when you are sick, use a mask without a valve.

- because in many settings you'll be using a mask without a valve to protect patients, the inside of the mask will get very damp. If the mask has not been tested for liquid resistance, then this can be a problem, as the fluid may seep through the mask over time, and then again risk infecting patients. If the masks are not tested for this, the filtration efficiency may also be impacted as the mask gets wet. Surgical N95 masks are tested for 2 way fluid resistance (to ensure no fluid from patients comes through the mask to wearer, and to ensure no fluid from wearer comes through to others)

- fit is very important. Surgical N95 masks are tested for fit and escaping/incoming airflow under normal conditions of use. Without this testing, and without a mask that fits well, HCWs and patients can be exposed.

Long story short, KN95 masks are still useful in many settings, and we need those too. But what we need even more is surgical rated N95 masks, ideally certified by NIOSH as such.

It's also likely that many of the masks that are rated as KN95 would pass liquid and fit tests if subjected, but without the testing and certification, I understand why many HCWs would demand certified masks to protect themselves and their families.

She also mentioned that she expects standards in hospitals to decline over time, and that they will eventually accept other mask types for donations, if they don't already.