Diapers smell musty after drying. Not a urine/poop smell, but there's definitely something there. This can be a few things. It could be that you didn't use quite enough detergent for that load. If it's a consistent issue, up your detergent a bit and see if that helps. I also found this can happen with detergents that are scented but not strongly scented.
Diapers reeeeeeeeek of urine. What's happening here depends on when they smell. Do they smell strong after being used as night time diapers? That is not necessarily something to worry about as it may have been the urine has been in that diaper for 6+ hours so it's starting to break down. Rinse it out before you put it in the pail and then remember to check it after you wash it to see if it still stinks. You may also notice a build up in the smell as they sit in your diaper pail for a few days. This also happens naturally as your baby gets older as they have more pee, and are typically changed less frequently. A newborn can be changed sometimes every 45 minutes so compare that to a toddler who might go up to 4 hours between changes. What kind of material are your diapers using? Microfiber is known to hold on to stink and the thicker it is, the harder it becomes to get fully clean and rinsed. That being said, any material with a ton of layers can run into this problem. Check your diaper and/or inserts to see what they're made out of. AIOs and some AI2s use microfiber as a quick absorbing agent. Something to try would be doing your pre-wash using warm water rather than cold to see if that helps break it down. You can also try running a couple loads with the offending diaps in hot water without detergent. If you still have issues after trying that, you may want to try stripping the diapers using a product designed for it specifically, such as Mighty Bubbles or RLR.
Diapers smell like barnyard, manure, hot garbage juice, etc. This smell is usually most apparent when they're hot out of the dryer. Basically it just means they're not getting clean enough. First, do either a Mighty Bubbles treatment or a soak in RLR according to their package directions. After that, your options are to use the recommended amount of detergent according to what they say for a heavy soiled load, if that doesn't work to try and see if it's a hard water issue by adding Calgon/washing soda/Borax, and if THAT doesn't work, trying a completely different detergent. If you are lucky enough to have soft water but are having stink issues, you might be using too much detergent. Try doing a Mighty Bubbles treatment to help break down any lingering detergent and then decrease it by half or so for the next couple washes.