Post-War currency

The currency in the Fallout world has varied from game to game.

Fallout 1 and 3: Bottle Caps
Bottle Caps are the standard currency in the first Fallout game. In Fallout 2 regular money has been introduced and bottlecaps have been rendered useless and can only be found in Broken Hills. Bottle caps make a return as the standard currency of the Capital Wasteland in Fallout 3. In addition to bottlecaps, a form of pre-war currency (most likely American Dollars) can also be found in the ruins of DC which can then be sold to merchants in return for bottle caps. Bottle Caps can also be put to use in weapon form as one of the major components of a Bottlecap Mine.

Bottle caps are backed by The Hub merchants. The reasoning for their support is that the technology to manufacture bottle caps and paint the surface has been lost in the Great War, which would greatly limit any counterfeiting efforts. Secondly, there is a limited number of bottle caps, which would serve to preserve their value to some degree.

The issue of some concern is that with time, number of bottle caps will decrease due to wear.

Hypothesis of Depiction
The graphics show bottle caps as having the rimmed edges pointing outward. This depiction is likely a production decision to communicate the "bottlecapness" to the player; in real life the caps would have most probably ended up flattened over the passage of time, or intentionally pressed to increase the carrying capacity for the individual. For Fallout 3, Bottle caps return as the main form of currency, most likely due to the Capital Wasteland's isolation from the more civilized western coast. Interestingly enough, one can also find pre-war money though it is simply nothing more than weightless loot that fetches a nice price. Also of note is that unlike previous Fallout games, when you drink a Nuka-Cola, its bottlecap is actually added to your stock.

Fallout 2: Gold Dollars
In Fallout 2 it was dollars backed by gold in value and being used by the 3 big powers of New California Republic, Vault City, and New Reno, bottlecaps therefore becoming little more than nostalgia as at least one of the three described powers had influence in just about any civilized spot in the Wasteland.

The town of Redding uses two different kinds of mine scrip that are basically equivalent to the more common gold dollar.

Fallout 3: Pre-War Money
Pre-war money is a junk item, appearing as a stack of paper notes. It can often be found in safes and cash registers.

Although it is of low value, it is weightless. Pre-war money may as well be taken and sold to a scavenger or trader. Or to be kept as ammo for the Rock-It Launcher, as it is weightless, you can never carry too much.

The reason for this being a commodity may be twofold - both as a plentiful supply of paper for pulping and recycling into useable materials, or to be stockpiled against the possibility that, if the US reforms, the currency will once again become valid. Also, let's not forget that it can, in a bind, serve as "rough on the edges" toilet paper.

Pre-War Money is found just about everywhere, in both public and domestic areas, as well as retail outlets such as the Super Duper Mart.

Money in Fallout Tactics
In Tactics, both Brotherhood scripts and Ring pulls are used, the latter essentially being the same as bottle caps: Ring pulls are pull-tabs from soda cans.

The Brotherhood scrip (or Brotherhood scripts) is/are a currency used only by the Midwestern Brotherhood of Steel for trade within the Brotherhood. Brotherhood traders accept only this currency with the exception of some outsider traders that are present in most bases and accept ring pulls.

Ring pulls are used by the Midwestern Brotherhood of Steel as currency when trading with outsiders (non-brotherhood). They are actually pull-tabs ripped from soda cans. Ring pulls can be found all over the settlements in early missions and traders will accept them. There are usually some outsider traders in Brotherhood bases who will accept ring pulls as well.

Ring pulls are probably used as currency for the same reason that bottle caps were used in the first Fallout game: given that they're harder to reproduce with post-war technology reduces the odds of counterfeiting.

Money in Fallout: BOS
Brotherhood of Steel uses Caps, though due to blatant product placement replacing the beloved brand Nuka-Cola, BAWLS bottle caps are worth extra).

Waluta