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In this article, we will discuss different ways to retrieve Jetton’s historical prices on Decentralized Exchanges, DEXes. Each swap operation, whether between a native asset (Toncoin) and Jetton or between two distinct Jettons, has its price, a fixed exchange rate of one asset to another. This price is calculated by the internal DEX math algorithm, called AMM. Some services require information about previous swaps on the blockchain to use it in their internal business logic or to simply show statistics to users.

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Off-chain API

The most common use case for the price API is to fetch Jetton info on the web2 backend and use aggregated data inside the service. There are several historical Jetton price providers in TON: You can find detailed information about API usage and technical details in the provider docs. There is no established solution for real-time jetton swap market data; however, one can explore CoinGecko websocket API.

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On-chain API

Currently, it is not possible to retrieve historical jetton prices on-chain - since TON contracts are limited by storage, it is quite hard to implement such an API fully on-chain. However, it is possible to retrieve current prices via the Request-Response pattern on some DEXes; refer to the specific service documentation to learn more about it.
Since the TON execution model is asynchronous, the jetton price might change between the moment of the response from the price provider and the moment the contract processes the response. Consider this factor in smart contract logic.
For example, on the DeDust DEX, it is possible to retrieve pool information on-chain using an internal message with the following TL-B schema: 
provide_pool_state#6e24728d query_id:uint64 include_assets:Bool = InMsgBody;

take_pool_state#bddd4954 query_id:uint64 reserve0:Coins reserve1:Coins total_supply:Coins
                         assets:(Maybe ^[ asset0:Asset asset1:Asset ]) = InMsgBody;
Here is a smart contract snippet in Tolk illustrating how you can send the ‘provide’ message: 
struct (0x6e24728d) ProvideDeDustPool {
    queryId: uint64
    doIncludeAssets: bool
}

fun main() {
    val requestDeDustPoolInfoMsg = createMessage({
        body: ProvideDeDustPool { queryId: 1, doIncludeAssets: true },
        bounce: true,
        dest: dedustPoolAddress,
        value: 0,
    });

    requestDeDustPoolInfoMsg.send(SEND_MODE_CARRY_ALL_REMAINING_MESSAGE_VALUE);
}