As far as European boardgames go, one of my best recent finds would have to be Colosseum. Designed by Wolfgang Kramer (El Grande, Tikal) and Markus Lubke, and published by Days of Wonder, Colosseum charges players with running an ancient Roman Colosseum over five rounds, or "days", and attempting to put on the best show possible during that period.
Each player starts with a colosseum. On each turn, players have the opportunity to buy one and only one investment, which range from colosseum size upgrades to new performance blueprints through to a loge for the Emperor. Then players bid on groups of tiles in the "marketplace" which represent assets for use during performances, such as gladiators, boats, lions or scenery. Finally players put on a performance, which scores points based on how ambitious the performance is, how many of the required asset tiles the player possesses, whether any consuls or senators came to see the performance, and a variety of other factors.
The first interesting part of the gameplay is that performance scores aren't cumulative - only your highest scoring performance over the five days counts. However, when you put on a new performance, each previous unique performance you've done counts for five spectators. Also, the investment system means you'll only be able to put on the epic productions in the final game turns.
Successful performances pay the money you'll need to expand and perform well during marketplace bidding. Being in first place also scores you free "podium" upgrades which provide additional spectators at your shows. However, each round the player in last place gets to take an asset of their choice from the leading player, which can be crippling. Deliberately setting your pace over the five turns is a critical component of optimum play.
The asset tiles themselves have interesting connections and assymetries. For example, every performance that requires "lions" also requires "cages", so investing in one without the other is a losing strategy. When you have "boats" you don't need a lot more to put on a performance, but they're an all-or-nothing gambit as they're not used in many programs and are needed in high numbers to be effective. Some asset tiles reward you with a "star performer" token when you have the most of that sort of tile in play, which guarantees you extra spectators when those assets are used.
The driving force behind the game, though, is the five turn structure, which forces you to be brutally efficient if you want to put on five shows in five turns. You start with only two shows you can perform, so you'll need all five turns to buy the three programs and two arena expansions necessary for optimum endgame. A system of "Emperor's medals" means that lucky players may get an additional expansion, providing they have the cash to pay for it.
The contents of the game's box are gorgeous, with a vibrant board, colourful cardboard components, and some painted wooden pieces depicting the Emperor, senators and consuls which are absolutely some of the cutest markers ever seen in gaming.
Games run for about an hour. The gameplay is very easy to teach to new players, and the included rulebook is easy to understand and well illustrated. Becoming competitive will probably take most people a couple of games, though, as despite some included reference sheets the relative merits of different investment strategies are not immediately intuitive.
The game supports three to five players, remaining equally enjoyable at all group sizes, and retails for $50 USD, or $60-85 AUD depending on where you buy. If you're tired of endless games of Settlers of Catan and are looking for something new and exciting in Euro-boardgaming, Colosseum is well worth your time and money.