I've always enjoyed playing a good simulator game. However, to make most of them fun, you have to take a few liberties with the mechanics of the game to make it work. For example, most city simulators let you place roads, power plants, zones, etc. under the pretense that you're the mayor. However, in the real world, a mayor doesn't have nearly that much power. Games tracking the rise and fall of civilizations have you ruling a civilization ... for dozens of times as long as you'd actually live.
This game makes no such leap of faith. Why are you able to exercise such control over your island of tropical paradise? Because you're a corrupt dictator, that's why!
I never played the second game, but it followed soon after the first with what seems to be a similar style, but pirate-themed. This review will primarily deal with the original game, from my own experience.
The game runs on the same engine as Railroad Tycoon 2, and it shows, primarily from the interface that is presented to you. You get mostly the same fonts, the same style of buttons, and the same annual-report-in-a-book-format that you get from the Railroad Tycoon series. Heck, the citizens of your nation sometimes ponder, "This place would be better if it had a decent train simulation."
At the beginning of the game, you get to select a ruler, each of which has a bunch of positive and negative traits. These can really make some of the scenarios more interesting, and playable more than once. Certain characteristics make you more popular with some and less popular with others. Also, each character has two flaws, both of which can be pretty severe, causing you to plan your strategy around them. For example, the cheapskate flaw, besides making you less appealing to some, also sets the maximum wage you can pay people. It can be difficult attracting the right talent to the jobs you need with that firm cap on wages.
The game comes with a sandbox mode as well as a bunch of scenarios. The scenarios have some twists to them, but the game plays out pretty much the same both ways. For sandbox mode, you get to pick your victory conditions, as well as some difficulty-setting parameters.
A typical game starts with you and a bunch of unskilled workers on your tropical island. You start out with a dock (for exporting goods as well as immigration and eventually tourism), a palace (for some initial military), and a workplace for each of builders and teamsters (they transport stuff). You need to build some farms for food, some houses for living (they live in shacks if you don't build them houses, and they aren't happy about the shacks), and some farms or mines to export goods to start off. Early in the game, you'll rely mostly on foreign aid for cash, later moving to exporting raw goods like iron ore and tobacco, and still later switching to processed goods like cigars and lumber and service for tourists.
Each of your villagers is tracked by the game individually, and has a name, desires, and some factions. There are several factions, each somewhat at odds with each other, though there are some natural rivalries, like capitalist vs. communist and religious vs. intellectual. Each faction has different desires, and you'll want to try to satisfy the majority of your population by pandering to the wants of the largest factions.
Every few years, your villagers will want elections. You can refuse to hold elections, but that can anger people, especially if they are already displeased with your performance. Keeping the military strong and pleased is especially crucial if you go this route, as they can help to keep everyone else in line. Get the military mad at you, however, and they'll stage a coup d'etat. If you do hold elections, you get a year to fix up your act against a single opponent with real-time polling data. If you address the biggest concerns of the population (or use a well-timed tax cut), you can sway the results of the election. If, when the election is drawing near, you fear that you may lose, you can rig the election, swaying the results significantly. It can't guarantee a win, but it's much more difficult to lose a rigged election. The rigged elections, though, cause you to lose favor with people, making the next election even harder if you don't have a plan to improve.
Over the course of the game, you will hopefully be able to grow your treasury, making your island empire rich. You'll typically want to siphon some funds off the top to your Swiss bank account for your eventual retirement (the game has a finite length). Your final score is based on the happiness and number of people on your island, the size of the treasury, and the size of your Swiss account---dollars in your Swiss account are worth much more than treasury dollars, however.
The game has a fairly complex economic system that drives everything. While you control which buildings get built where, what wages each job pays, what rent costs in each apartment, etc., you don't get to order the villagers around directly. Getting them to do what you want them to do is all about creating incentives for them. Pay higher for the jobs that they don't otherwise want to do (whether they're too far away, or require too much education, or just aren't satisfying enough), and they will switch over. Charge higher rent for the nicer accommodations, and you will be able to satisfy the communist faction (passable housing for everybody) and the capitalist faction (nice housing for the rich).
I haven't gone into a lot of the systems for the game. There's an education system to get skilled workers. There's an electric system for increasing productivity and luxury. There's a health care system to prevent premature death, increase people's lives, and increase the birth rate on the island. There's a diplomacy system where you have to balance your relations with both the US and the USSR. These continue, and the whole thing is interrelated, but still pretty natural to understand. You can speed up or slow down the game to whatever pace you're comfortable at. There are piles of data in the yearly reports to pour through (or not), so you can try to pinpoint exactly what is going wrong with your little corrupt republic. You can also just click on people and examine their thoughts to get a good idea of where you're succeeding and where you're failing.
I had a lot of fun with this game, and keep in mind, I've only played the first (without the expansion). The expansion adds several new scenarios as well as a bunch of other stuff, and then there's the sequel with it's wildcard of a pirate theme. The demo said about the game "there should be more than 50 hours in this game to spend at your keyboard, smoking a cigar." While I wouldn't recommend smoking at your computer (the tar makes the insides nasty), I'd agree with their assessment---and I found it fun, too.