This review is for single-player only.
COD 4: Modern Warfare is a "roller coaster shooter." What is a roller-coaster shooter? It's a shooter game whose gameplay and level design are focused around linearity and setpieces. Instead of wandering and backtracking through a mazelike environment, you move in a generally straight line from scripted event to scripted event. It's the kind of game that makes old-school gamers cringe, because it dispensed with the relatively cerebral, game-y feel of Quake, Doom, etc., and replaced it with something closer to an interactive movie or Time Crisis.
Although the roller-coaster shooter trend arguably began with Half-Life, the genre reached its peak in the late '00s and early '10s. There were plenty of roller-coaster shooters on the market, but none made such a big impression as the Call of Duty: Modern Warfare series. And with good reason. While plenty of other devs tried to do their own roller-coaster shooters, Infinity Ward was one of the few studios who nailed it. Plenty of developers followed the linear corridor-cutscene-corridor design like a cargo cult, but Infinity Ward was tone of the few to understand how to actually make it work. And the way that they made it work was essentially by making the game feel like an interactive movie, in the best possible way.
Each mission in the game has some sort of gimmick, whether that be a certain weapon, a unique objective, or a different style of gameplay, such as coordinating airstrikes. Additionally, the missions are paced like an action movie. We have brief breaks in between missions for exposition, there are one or two memorable setpieces in each mission, and every mission advances the plot in some way, so you want to find out what happens next. It's a very basic formula, but compare it to snoozefests like Horizon Zero Dawn or Nu-Raider. There are sections in Modern Warfare where you basically just hold the left stick forward, but they are always put in the context of something exciting, like sneaking past enemies. There are plenty of cutscenes, but they are always short, always involve something exciting, and always drive the plot forward. You won't see people just standing around talking about their feelings. There's a sense of urgency in the game that allows you to look past a lot of the shallow mechanics and story. Say what you will about Infinity Ward, they nailed the pacing of the game.
The art direction in this game is phenomenal, especially considering that it came out during the 7th-gen "uncanny valley" years. Sure, the art style is "gritty photorealism with earth tones," which may or may not be some people's cup of tea (arguments to the effect that people who don't want to play as cartoon characters are immature will always amuse me), but the game does a better job of the art style than almost any comparable game from the time period, including the Gears games. Compare it to, say, Rainbow Six Vegas 2, a game with a similar art style and graphics, but whose art direction is far worse.
Unfortunately, I can't speak as highly of the gameplay itself. Modern Warfare games have a huge readability problem; to put it simply, it's really difficult to figure out what is happening onscreen. This is compounded by the Bloody Screen!, which has to be one of the worst design trends in the history of gaming. The Bloody Screen! obscures your vision at the very moment when you need it most, turning being low on health from a moment of excitement to a moment of frustration. Additionally, I found it very hard to keep track of who was shooting me and where, which led to lots of encounters that were more irritating than fun. The gameplay has other flaws as well, most of which are flaws of the roller coaster shooter genre at large. There are also issues that I have with the story, which I will deal with in the next section of the review.

Short essay on violence and propaganda in COD 4.
Note: this essay delves into some political topics. Skip it if you are not interested.
As much as I'm not on board with the "America Sucks Sweepstakes," I can't help but feel like I'm playing a particularly callous piece of American propaganda when I'm playing this game. I can stomach propaganda when it's over-the-top and clearly fantasy. Dick Freedom throat-punching Fritz Sturmkampf and Ivan Badnik while "The Star Spangled Banner" plays in the background might be intended as propaganda, but it's so unrealistic and over-the-top that it's hard to take seriously. Battlefield: Bad Company 2 had a "rah-rah America!" storyline, but it felt more like a popcorn action movie than a comment on foreign policy, and thus I gave no thought to any politics (real or imagined) involved in the plot. I like military-themed games, I've played a fair bit of them, and taking the storyline of most military games seriously would be an act of silliness on par with the "video games cause violence" line of thought.
Call of Duty 4, though, just felt different. I've played lots of "violent" games and none of them felt as sadistic as Modern Warfare. The game begins with a mission called "Crew Expendable," based on your handler's instructions. "Sweet dreams," says Captain Price as he shoots two of the sleeping crewmembers. We have a scene where you provide air support while joking about killing the combatants on the ground. There's a torture scene that ends in Captain Price killing the "terrorist" he's interrogating because…well, I'm sure he had good reasons. It's callous, it's in your face, and it's presented as very serious (as opposed to, say, the wacky hijinx of the ultraviolent Rage 2, or the clearly fictional nature of a zombie game). I start to wonder if the game's designers were "encouraged" by some governmental entities to work in some storylines that make torture and extrajudicial killings look glamorous, or at least justified.
The "game-as-propaganda" theory even makes sense of one of COD's more frustrating design decisions--the fact that most of the game consists of you following around more important characters, doing what they tell you to do, and watching as they do something cool. When you think about it, doing what people tell you to without questioning it is a large part of the military experience. Instilling this obedience, this loyalty to the group rather than the individual, is part of the point of boot camp, basic training, etc. It's not necessarily that the game's insistence that you do the missions in exactly this way is a nefarious propagandistic element--it adds an element of military "realism," and makes the missions easier to program--but it does seem to be compatible with the game's possible aim of making young men amenable to the goals and methods of the American Military.
None of this is to say that you shouldn't play the game, or that the game is only propaganda. It's just something to think about. You're an adult--come to your own conclusions.

Score: 90/100

Story: 9/10
Great story with brilliant characters. I will never forget Captain Price, Gaz, Nikolai, and even Sgt Griggs. The devs making you die after the nuke goes off was definitely the right decision after a good few missions where you get to become attached to your main character.

Gameplay: 10/10
So much variety. Before your general shootouts become boring or overdone, you switch to a turret section, an assassination mission, or a stealth mission. The gunplay is great and the controls are slick. Some of the greatest call of duty missions (from what I've heard) are in this game. All ghillied up for example is spectacular, giving you a choice whether to kill soldiers or walk past them, staying prone in the grass as soldiers as walk by, it is so tense and I love it.

Graphics: 10/10
Judging by 2007 standards, wow. This game looks fantastic, all you need to do is look at the nuke scene.

Soundtrack: 8/10
Not as good as black ops 1 or MW2's soundtracks but still damn good. A lot of iconic themes in this one.

Sound Design: 9/10
So good for 2007, Guns sound great, with all of them having their own unique sounds. It's just really good.

Artstyle/Art Direction: 7/10
Some very good art direction in a good few areas, but a lot of the time it can just turn into a mixture of dark greens, greys, and browns.

Extras: 9/10
While simple, the multiplayer, especially with friends, is a blast and so much fun.

Fun Factor: 10/10
I love this game, it's so much damn fun. Great characters, a great story, and a variety of gameplay sections in the campaign make this game one of my favourite FPS games and one of my favourite games of all time.

I highly recommend this game to literally everyone.