What is going on?
Once you have smoke physics set up (with a domain & flow object) and play your animation, Blender automatically calculates the smoke effect for every individual frame. There is no notification or progress bar to let you know this calculation is in progress. Once the calculations are complete, then the smoke/fire will play whenever you play the animation. The more complex your .blend file is, the longer this calculation takes. Most often, you actually have working smoke - you just haven't waited long enough to see it.
What is the solution?
Option 1: set your animation to a short number of frames before you try to play the animation - this could still take a long time depending on the complexity of your scene
Option 2: create your smoke/fire in a new .blend file and append both the domain and the flow object into your animation file
Option 3: just wait for a long time and work on another area of your animation while you wait
