I use a Roland R-05 handheld digital recorder to capture songwriting ideas, both lyrical and musical:
https://www.roland.com/us/products/r-05/Tascam, Zoom and other companies make similar products.  You can use the voice recorder on a smartphone also, but it's more difficult to use and more difficult to transfer files off of.  The Roland is so easy.  When I'm in creative mode, I don't want to have to think too much;  I want to just press a button and record.  Also I like to have a dedicated device for songwriting, rather than a jack-of-all-trades cellphone.
-Tre

 Listening to: 
Jesse Winchester