18xx is the collective term used to describe a set of railroad-themed stock market and tile laying games. The 18xx set has two main branches: the 1829 branch (1829, 1825, 1853, and 1829 Mainline) and the 1830 branch (1830, 1856, 1870, etc). There are also a number of crossover games which sit somewhere between the two branches (eg 1860). While general railroad operations such as track laying are critical to both branches, the two branches are fundamentally quite different in character and player focus. The 1829 branch games emphasize stock-picking and portfolio management while the 1830 branch concentrates more on financial prediction and stock market manipulation. So in 1829 et al. players are rewarded for holding the right stocks at the right time and for running their companies well, while in 1830 et al. they are rewarded more for manipulating the stock market to their advantage and investing in the companies that thereby profit.
The original 18xx game from which all others trace their design lineage is Francis Tresham's 1829.
The games mostly involve railroads/railways. (The exceptions are games like Ur:1830 BC and 2038, which are based on the 18xx system, but have a different theme.)
Highest net worth (normally cash plus stock assets) determine the winner.
Players can buy stock in companies.
The player (or corporate entity, e.g. in 1841) with the most stock runs the subject company as president or director.
Turns alternate between stock buying/selling rounds and operating rounds.
In operating rounds, the president/director determines what track tiles to lay and where and what stations/bases to create, calculates the earnings of trains, decides whether to pay out the revenue as dividends to the shareholders or to retain it in the company, and may buy a new train. These don't necessarily have to happen in this order (e.g. train buying may occur before revenue calculations in some games).
The purchase of new types of trains may trigger changes in the games (increased revenues, border changes, private company closures, new track tiles, etc.).
The board has a hexagonal grid and track tiles are hexagonal in shape.
Stock values rise or fall depending on whether revenues are paid out as dividends or retained by the company, and/or whether stock is bought or sold.