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Pros
Pro Extremely easy to build a quick prototype
Even though it's pretty minimalistic out of the box, Flask still provides the necessary tools to build a quick prototype for a web app right after a fresh install. With all the main components pretty much packed in the flask
package, building a simple web app in a single Python file is as easy as it gets.
Pro It is minimalistic and straightforward
Often you are not even aware of all the steps that the framework does in the background (a good example is Rails). Flask is very much straight-forward about what processes take place, so when you learn it, you become very proficient and don't lose any skill even when changes or updates are implemented that disrupt the usual workflow.
Pro Minimalist without losing power
Flask is very easy to get up and going, with vanilla HTML or with bootstrap pieces. It doesn't take much lines of Python to load Flask to get headers working, etc, and since it's all modular you don't have to have something you don't want in your application.
Pro Very flexible
Flask gives developers a lot of flexibility in how they develop their web applications.
For example, the choice of not having an ORM, but instead choosing one suited to the task, or another area where Flask gives a lot of options to developers is the templating. They can use Jinja2, Flask's default templating language or choose from a number of different templating languages they desire.
Cons
Con Requires some expertise in programming
If you are not heavily into programming and don't want to think about how stuff works in detail, learning how to use Flask can be too much. You would probably be better off using frameworks that hide most of the nitty-gritty details from you.