Ah, Engines. The mysterious things which drive us to school, work, and home every day. But how do they work (as specifically relates to physics)?

 In thermodynamics, an engine consists of three main parts:

• The Hot Reservoir, which provides energy.
• The Heat Engine, which converts heat into work— usable energy.
• The Cold Reservoir, which sinks unused, inefficient energy into the environment.

In case that's hard to understand, here's a diagram:

 Historically, engines have been quite important to society's evolution. For instance, take the Steam Engine. This wonderful invention catapulted humanity from being a bunch of bugs on a rock to being an industrialized powerhouse. Steam Engines were the first meaningful (don't forget waterwheels) forms of engines. Within a Steam Engine, coal is used to heat fire, such that water forms a hot reservoir, and then the pressure generated by the Steam within the engine is used to perform work, before being vented into the atmosphere, which forms the cold reservoir.

 However, let's take a closer look at normal, everyday gas engines. In a gas engine, gasoline is pumped into a cylinder, whereupon it's compressed. Then, once compressed as much as possible, a spark plug ignites it. Since this turns the gasoline from a solid into a gas, its density decreases and thus pressure increases. Finally, the pressure upwards is used to perform work, while the fumes are vented out into the atmosphere. In this example, the gasoline's unlit chemical energy forms the hot reservoir, the piston extracts work (and thus acts as the Heat Engine) and the atmosphere forms the cold reservoir. However, and remember this for later: because the gasoline is ignited by a spark plug, the efficiency is lower, since not all of the gasoline might be ignited.  Something to note is the processes that the gas is under throughout ignition:

1. AB: At first, the gas is drawn in via an isochoric process, where the volume remains constant. During this, pressure might dip as it's almost literally sucked into the cylinder.
2. BC: Once in the cylinder, the piston comes down and compresses the gas in an isothermal process, where its pressure goes up while its volume goes down. Finally, there's a spark, and the gas ignites!
3. CD: Once lit, the gas is under an adiabatic process, where the gas expands, while its pressure remains constant. (In this case, the pressure drives the piston up.) The temperature also declines a bit.
4. DA: Finally, the gas cools and is pumped out in another isochoric process.

All in all, here's an animation of that process, accompanied by the gas's Pressure vs Volume graph:

Keep in mind that this animation is pretty rough; that graph is pretty much an educated guess at the end. The other thing to note is that a combustion engine actually does a non-reversible process; the gas can't be un-combusted, after all.

"But what about the future? Aren't Electric and Diesel engines going to save us from climate change?" I hear you ask.

First, let's examine Diesel engines:

 In a diesel engine, the fuel isn't ignited by a spark, but rather by the immense pressures generated by the piston pressing down on the gas. (Look, see! I said it'd come back later!) Because of this, it's less complicated and tends to be more efficient. Additionally, diesel engines use diesel fuel instead of gasoline— because diesel is more power-dense, this also helps with power generation and fuel efficiency, too.

Next, in electric engines:

 For electric engines, rather than it being chemical energy, it's electric potential energy which is converted, not via internal combustion, but via a motor, to work. In an electric engine, a few additional challenges are faced:

• Maintaining an electric charge; is it from a typical internal combustion generator? Or is it from a battery? Maybe even both? How much mass do either of those add? What about cost?
• Figuring out how many motors to use, and if so, in what configuration; is there one motor connected to a transmission? Or is there one motor for each wheel? How does this effect costs?

One final thing to think about for electric cars is the vast diffference in efficiency between them and typical combustion engines; where a Disel engine might effectively use about 30% of the energy in its fuel, and Gasoline engines use about 25%, an electric car can effectively use up to 100%!
(Note that it's not actually 100%, because it's impossible, but you get the point! It's really efficient!)
 This is because electric cars can utilize regenerative breaking to turn kinetic energy back into electric potential energy when stopping; a source which is usually turned into heat by a conventional car's breaks. Secondarily, because electric cars also use electric motors (duh!) instead of combustion engines, the waste heat produced is a lot lower. Electric cars also have a lot of other benefits, like being quieter and more convenient because they can be refueled (so to say) at home, rather than having to go to a gas station. Some electric cars can even be charged on normal household wall outlets!

Sources:

• afdc.energy.gov: How do Disel Cars Work?
• mbofbakersfield.com: Learn About The Difference Between Gas & Disel Engines
• fueleconomy.gov: Where the Energy Goes: Gasoline Vehicles
• fueleconomy.gov: Where the Energy Goes: Electric Cars