This guide is very similar to the Blender Smells Like Burning guide. It's worth referencing if there are smells but not any smoke...yet.
We know that smoking is bad for your health, so when your blender starts smoking it's necessary to stop blending and find the cause of the smoke.
Burning implies the presence of undesirable friction, and smoke is a symptom of too much friction. When this smoke travels past or through your blender, the food inside can become contaminated. We suggest not consuming this food. This page is full of the possible causes for a smoking blender, along with tips for solutions, including parts and guides for repair.
Food Buildup Clogging Blades
Check the container for any food particles that may be obstructing the blades. Blenders need to be cleaned immediately after use with warm water and soap to prevent food from drying in and around the blade shaft. As the shaft begins to spin, the dried food will begin smoking.
A blender that is working too hard processing frozen foods, hard nuts, thick butters, flax seeds, cell phones, glow sticks, etc. will be working harder and may eventually burnout or stall.
Your blender may be equipped with a thermal breaker that shuts down the motor if it starts overheating, so while there's little risk of fire, the blender still might start smoking. If the blender is running for more than a minute on a low power speed, it's likely the motor overheating. Let the blender cool down.
Blade Assembly Failure
The blade assembly is made of two parts typically: blades and bearings. By blending hard objects, blades will dull and cause the motor to work harder and overheat. Blades last an average of 6 months with moderately heavy use. Sharpen or replace the blades if they are dull.
The bearing inside the assembly may also fail from overuse and misuse. Some blenders, like the Vitamix, are intended for running at their max speed in order for the cooling fans to properly work. In some cases, the bearing seal may melt or otherwise disintegrate. Water will then infiltrate the bearings during cleaning and wash away grease and cause rust to form. Replace the bearings or entire blade assembly if the blade won't spin.
Blade Gasket Failure
You can run a simple test to see if your blade shaft gasket has failed. Fill your blender 1/3 of full with water, and run the machine on high for a minute. If the water becomes dirty or brown, oil is leaking from blade assembly into the cup. Oil leaking in means that food is leaking out through this same hole. Replace the blade assembly.
Cup Gasket Failure
Inspect the gasket on the inside of the cup for wear. If the gasket is loose, cracked, or worn, replace the gasket. A failing gasket can allow a leak to infiltrate the motor housing and short the motor.
Drive Gear Melting
If your blender is experiencing too much friction or the pitcher isn't aligned on the motor coupling, the gear on the motor shaft may be stripping the plastic coupling. Reseat the cup, or replace the coupling.
Maintenance and Replacement Parts
Most modern blender manufacturers do not offer replacement parts beyond pitchers/jars/jugs, gaskets, and blade assemblies. While it may be hard to replace individual bearings or sharpen blades, these fixes may be the more economical solutions.