I disagree with the existing answer. There is very little exchange rate risk.
Stocks have an inherent protection against exchange rate fluctuations.
Consider when USD strengthens when compared to EUR. This means your investment will increase in value as measured in EUR -- or will it? It's not that simple.
The competitive advantage of US-based companies reduces when USD becomes stronger. Thus, European companies will steal some of the business of US-based companies. Therefore, your investment as measured in USD will decrease in value. This decrease in value as measured in USD will at least partially offset the increase in value as measured in EUR.
Furthermore, most big companies nowadays (S&P 500 is made of big companies) are internationally diversified. So, a company with headquarters in US will likely have business in Europe, in emerging markets, etc. So the profits will have to be converted from euros and emerging market currencies to US. Then you are converting the profits from USD to EUR. Part of the profit was originally in EUR, and undergoes dual conversion (EUR -> USD -> EUR). Yet another part of the profit was in some other currency. Only part of the profit was in USD.
Some stock funds hedge against this (nonexistent) "exchange rate risk". Fortunately, there are only little of these exchange-rate-hedging funds. No intelligent investor will buy an exchange rate risk hedged stock funds. However, exchange rate risk hedged bond funds might make sense -- or then you can buy bonds only in your local currency to avoid the exchange rate risk altogether.