Product review (1 stars): It fits, does NOT perform
First, I do not write many reviews.  I am just a buyer, not affiliated with any companies or organizations.  I feel so many reviews are fake and misleading.
I have never really thought much about the tap water as the official city water reports make it sound like the water is safe - and I'm sure it ...
So, I have an older Kenmore refrigerator - a Coldspot model.  This water filter seems to fit well.  I live in Phoenix, AZ in the city.  I have never really thought much about the tap water as the official city water reports make it sound like the water is safe - and I'm sure it is according to official "government" approved levels - whatever those are.  So I purchased this filter wanting to see and taste the difference.  I also bought a water PPM tester  https://www.amazon.com/gp/product/B073713G5F/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1 (it says Amazons choice with very good reviews).
So, here is my initial testing results, some really shocked me.
Costco (Kirkland brand) bottled water PPM = 23
Phoenix Tap water - PPM = 498
Water on the refrigerator AFTER flushing well over 4 gallons of water through this new filter - but installed same day as testing.  PPM = 476

I have not tried drinking it yet so cannot attest to the flavor of the water, only the readings from the PPM tester.  All water tested was at room temperature, I tested each water immediately after opening or pouring, and also filled 3 separate bowls with each respective water and let sit for 2 hours to eliminate any temperature differential, same results for each of the waters. I can also confirm the packaging my water filter came in DOES say NSF 42, 51, and 401 (I think I have those numbers correct).
So my review so far is waste of money.  I will update this review in about 2 weeks, after the filter has had time to really get set in.  I also emptied my ice bucket so all ice will have been filtered through the filter.  I plan to melt some ice in a bowl and test that water also since that's probably the biggest reason I bought this filter, living in Phoenix we use ice all day everyday.  Hope this review helps.  I do highly suggest the water PPM tester referenced above, it's not expensive and gives a good accurate (as far as I can tell) reading.  If you care enough about water filters, a good tester should help you know what you are paying for.

Update:  5/14/2018.  I am dropping my review of this filter to a 1 star.  I have flushed over 30 gallons (using 5 gallon water bottles) through the filter, using my tester on each bottle.  It has slightly improved over the tap water results.  Tap water is still 498ppm.  Now the filtered water is 462ppm.  So I read the data sheets for the filter, and it's level of certification and filtration.  I still had questions, so I spent the last 3 hours on the phone with EveryDrop by Whirlpool.  I was transferred to 5 different people, because they are all just sales people.  I asked to speak to someone with manufacturing, product quality, etc..  There is no one available or that I can leave a message for or anything.  They do not have anyone the consumer can speak to that can ask any questions beyond what is written on the package.  I asked what is a realistic ppm reduction performance of the filter - they do not know.  I asked when was the filter design last tested by NSF for certification - they do not know.  I asked for any material to show it's testing status to be certified NSF, they do not have it.  I think the filter is not certified, or even tested.  They could not show any evidence of any kind their filters are certified.  They also only referred to their own in house documentation to convey it's performance.
So after spending almost $50 for this filter, I see very little reduction in ppm (parts per million), and even the company cannot answer any questions aside from typical sales questions.  Ask them anything more detailed, they are lost.  Highly disappointed.  I will stick to the $10 filters, at least with those I have a very low expectation.