Now is the exciting time where I share my knowledge about armpits! Lucky you!
In the bathroom, when we decide to go zero waste, we often start with what makes more sense : the shower gel and shampoo, logically because these are the biggest waste creators. After this come naturally toothpaste & brush, and... deodorant. Socially crucial.
There are many option out there, I will try to share my experience!
First of all, in all honesty, I couldn't find any solution being as effective as a good old plasticky deodorant of the supermarket, called antiperspirant, which contains aluminium salts. I personally decided to avoid them as they have been linked with breast cancers and Alzheimer's disease, but no study has proven it formally apparently. No study has proven them harmless, either.
1. Alun stone

Truly last FOREVER. It is a natural stone (aluminium potassium and NOT aluminium chlorohydrate which mostly used in conventional anti perspirant deodorant in the supermarket) and doesn't penetrate the skin as much as the conventional antiperspirants.
Advantages : really great in travel. Lasts ages, hence it is probably the cheapest solution ever.
Cons : I didn't find it very effective... But a lot of people do.
2. Plastic free (paper) sticks

There are many brands out there, with natural ingredients, smelling fab, looking gorgeous, and plastic free. Not entirely zero waste though. If you look at the INCI (the list of ingredients) you will always find a hard fat base (coconut oil, shea butter etc... but in their scientific names, i.e. Cocos nucifera oil), an absorbent powder (Ex : arrow root powder), some bicarbonate of soda, and perfume. This is a great combination in my taste, but people with a sensitive skin might find it too irritating. There are a lot of brands out there, Ben&Anna, Posy, etc... and they usually costs about £10 each.
3. DIY
This is a quick recipe to do (5min), lasts long, is effective and really cheap. I like it because I always have these ingredients at home so it is very practical. In case of a big stress though, it did let me down, but nothing could have saved me apart the chitting Dove spray I had at work in my draw :) It melts above 25 degrees so it is better kept in a closed little jar. Many recipes include some drops of palmarosa essential oil - I personally add some lemon essential oil or Jasmin - or even nothing. If you want to use essential oil, please check well their effects (most of them are harmful to children below 7, and pregnant/breastfeeding women). It is basically very similar to the natural plastic free deodorant mentioned above - but truly zero waste as you probably would reuse an old container ( you can also use a coffee cup...) and already have the other ingredients anyway.

Simply melt under low heat all the ingredients together until melted and pour in some little clean jars (previously sterilized with boiling water).
- 3 tbsp of coconut oil
- 2 tbsp of cornstarch
- 2 tbsp of bicarbonate of soda
- 3 drops of jasmine ess. oil(opt.)
Apply a pea size under each armpit, with your finger or … reuse a former ice stick for example?!
Some people also just use bicarbonate of soda as well which is probably even easier!
Let me know your tips in the comments or on the facebook page!