For the target cell press Ctrl+Enter . Alternatively, you can
click the. icon and select Run Cell. ...
To execute all code cells in your notebook, click on the
notebook toolbar or press Ctrl + Shift + Alt + Enter .
To run all code cells above the 
current cell and handle possible code dependencies, click.

For the latest jupyter notebook, (version 5) you can go to
the 'help' tab in the top of the notebook and then select the
option 'edit keyboard shortcuts' and add in your own customized 
shortcut for the 'run all' function.