The first thing to decide is whether you want an electric pencil sharpener or a manual pencil sharpener. The former require less effort to sharpen a pencil, using a helical cutting mechanism that turns using electric power. The downside is that of course they require power, be it batteries or a wall socket. They also tend to be more expensive. Manual pencil sharpeners need hand winding but are fully portable and usually cheaper.
Once you've made that decision, you'll need to consider what kind of pencils you need to sharpen, and how often you'll be sharpening them. In our guide to the best pencil sharpeners above, we've noted the size and type of pencil that each sharpener can be used for. If you use your pencil for art, you're more likely to want to spend a bit more for a sharpener that will keep them in good shape.