Inventor is, like Ghost Hunter, a profession that comes with the Ambitions expansion pack.  This means that you are basically self-employed, although you have to register with the city.  The city apparently is also what evaluates your progress and grants you promotions, in case you were wondering how you get promoted when you're self-employed!

Unlike the other professions, there is only one thing that lets you level up as an inventor, and that is the amount of money that you earn from your inventions.  You have to earn more for each level, which makes each one harder to get through.

This creates an interesting experiment in microeconomics.  As an inventor, you have two ways to spend your time: creating things that you already know how to make, or inventing new things.  The first few things you invent are cheap little toys which are only worth $5 or $10.  In order to level up, you would have to crank out an awful lot of those!  

But you are going to reach a certain point where you want to level up, but you also want to invent some of the cool stuff.  I reached this point when my Sim had invented the Floor Hygeinator (which is worth about $150) but I really wanted to invent (and play with) the big items: the Miner and the Time Machine.  

There are only so many hours in a Sim's day, just like ours.  I had to choose between having my Sim crank out Floor Hygeinators to sell in order to advance his career, or stagnate on the career ladder in order to invent and create cool stuff.  It wasn't an easy choice, and there's no right answer!

One benefit to the Inventor profession is that you do make some pretty cool stuff.  The Floor Hygeinator releases a poof of pretty smell when a Sim walks over it, which gives them a positive moodlet.  Except for those times (probably when your mood is too low) when it releases a green fart cloud, which gives your Sim a negative moodlet.  

The Miner and the Time Machine are pretty awesome, too, and probably worthy of a post on their own.
In order to Invent, your Sim needs to have scrap material.  You can buy this scrap directly from the workbench for a ridiculously high price.  ($550 for 100 scrap!)  Or you can forage for it at the junkyards for free.  My Sim can pick up 100 scrap in half a day, which makes it really worthwhile to make a trip to the junkyard.

Confusingly, there is also an Inventor skill, which is separate from the Inventor profession.  Inventing things improves your Inventor skill, even if it doesn't advance your Inventor profession.  Oh, and there's also a related trait, "Eccentric," which lets you invent cool stuff faster.  Yeah; it's complicated.

The first five levels, and the amount you need to earn to level up:
1.    Electrocution Victim, $30
2.    Nuts and Bolts Combiner $75
3.    Duct Tape Rigger $225
4.    Whatchamahickey Designer $920
5.    Experienced Innovator $2500