Exchanges without order books price assets using a formula over pool reserves, and everything that follows is a consequence of that formula.

The constant product rule

The best-known design keeps the product of two reserve balances constant across trades.

Which means the price is the ratio of reserves and moves as the ratio changes.

Buying one asset removes it from the pool and adds the other, which raises the price of what you are buying.

Slippage

The price moves during your own trade, and the effect scales with trade size relative to pool depth.

Which is why large trades in shallow pools execute badly.

The curve is a hyperbola, so the effect is not linear and worsens sharply for large trades.

Where the price comes from

The formula does not know the market price — arbitrageurs bring it into line.

Which means the pool tracks external prices only because it is profitable for someone to correct it.

Those profits come from liquidity providers, which is the mechanism behind the next point.

Divergence loss

Providing liquidity produces a worse outcome than holding the assets when prices move.

Which follows mathematically from the pool rebalancing toward the falling asset.

The common term for this understates it, since the loss is only impermanent if prices return to the starting ratio.

Fees earned may or may not exceed it, and this is the actual question for a liquidity provider.

Concentrated liquidity

Later designs let providers allocate capital within a price range rather than across the whole curve.

Which improves capital efficiency substantially and requires active management.

Capital outside the current range earns nothing, so a position that moves out of range stops working.

Stable pair curves

Different formulas suit assets expected to trade near parity.

Which provides low slippage near the peg and behaves differently when the peg breaks.

The behaviour during depegging events is where the design differences become consequential.

Value extracted by ordering

Because transactions are visible before inclusion, they can be front-run or sandwiched.

Which is a substantial and measurable cost borne by ordinary traders.

Slippage limits, private transaction routing and batch auction designs are the main mitigations.

Reading a pool

Depth, fee tier, volume relative to liquidity, and what the assets actually are.

This is technical explanation of mechanism, not a recommendation to provide liquidity or to trade.

Fee tiers

Pools charge a fee on each trade, distributed to liquidity providers.

Which is set per pool, with different tiers suiting different volatility profiles.

Stable pairs use low tiers, since divergence loss is small and volume is high.

Routing

Aggregators split trades across multiple pools to reduce total slippage.

Which frequently produces better execution than any single pool would.

The trade-off is higher gas cost, so routing benefit must exceed the additional execution cost.

Just-in-time liquidity

Providing concentrated liquidity immediately before a large trade and withdrawing after.

Which captures fees without bearing ongoing exposure.

It reduces returns for passive providers and is a documented consequence of concentrated liquidity designs.

Oracle use of pool prices

Pools are frequently used as price sources by other protocols.

Which creates the manipulation vector discussed extensively in incident reports.

Shallow pools used as price references have been the proximate cause of substantial losses.

Providing liquidity in practice

The return is fees minus divergence loss minus gas costs, and whether it is positive depends on the pair and the period.

Which means published yield figures showing only fee income are incomplete.

Tools exist to calculate historical outcomes for a position, and they are more informative than advertised rates.

Comparison with order books

Order books express intent at specific prices, while pools express a continuous curve.

Which makes pools capital-inefficient for tight spreads and operationally simpler on-chain.

Hybrid designs and on-chain order books exist where block times permit them.

Before providing liquidity

Understand the pair's volatility, the fee tier, the expected volume and what happens if one asset fails.

This is explanation of mechanism rather than a recommendation.

New pool risks

Pools for newly created tokens can be constructed so that selling is restricted or fees are extreme.

Which is a common pattern in fraudulent launches.

Reading the token contract before trading is the check, and it takes minutes on an explorer.

Liquidity removal

Pool liquidity can be withdrawn by whoever provided it unless locked.

Which is the mechanism behind a well-known category of fraud, and lock status is publicly checkable.

Fee revenue reality

Fee income concentrates in a small number of high-volume pools.

Which means most pools generate little relative to the exposure taken.

Historical data for a specific pool is publicly queryable and answers the question directly.

Closing

The formula explains the experience, which is why it is worth understanding first.

Slippage settings

A tolerance that is too tight fails, and one that is too loose invites sandwiching.

Which is a real trade-off rather than a setting to maximise.

Private submission routes reduce the need to loosen it.