ESP 01: Sketch uploading but not running
The ESP8266 has different boot modes. i.e.

  

The ESP-01 module will keep booting into uart programming mode if gpio-0 is connected to GND. You can verify this by taking a look at the serial monitor output while powering up or resetting the esp8266.

In order to fix this, after the code is uploaded, you need to connect gpio-0 to 3V3 and reset the esp8266 in order to see the code running on the module.