Scrollable List Component from Material-UI in React
I just found out that you can add properties. 'maxHeight' and 'overflow' are the ones I was needing to solve my problem. For example for a List in a Paper container:
<Paper style={{maxHeight: 200, overflow: 'auto'}}>
<List>
...
</List>
</Paper>
This works if you want the list to fill all height of the container:
<List style={{maxHeight: '100%', overflow: 'auto'}} />