Google's new ALLO messenger claims to be very secure. It utilizes end-to-end encryption in the Incognito mode. Any messages transmitted in the Incognito mode will not be stored. Any messages not using the Incognito mode will be stored by Google to help with Google Assistant. Storing messages will help Google Assistant become more intelligent by using people's conversations to learn conversational language.
If privacy is your main concern you may want to find a different messaging app. If you are using the Incognito mode you won't be able to use the built in Google Assistant. Google Assistant is really what makes ALLO worth using. It can listen for key words in conversation and recommend places of business in response. Apparently there is an option to delete stored messages within the app if you wish to use Google Assistant and remain private. I am personally not worried about the "privacy concerns".
via Verge