There are currently 17 members of the euro area - all of whom are also in the EU. It is obligatory that members of the EU be in the eurozone, however they do have to meet certain requirements. There are 10 EU member states that do not use the euro as their sole currency, of these 10, 7 have yet to meet the requirements and will join when they meet them, and the other 3 (including the UK) have opted out.
There are reasons for these opt-outs, as membership of the euro area does constrain national economic policy in a number of ways. The first and most obvious way is the loss of control over monetary policy once you join a monetary union (such as the eurozone). Monetary policy in the euro area is conducted by the European Central Bank (ECB), which is located in Frankfurt. The ECB controls the base interest rate for the euro, and also holds reserves which it can use to bail out failing members of the eurozone if necessary to help the economic well-being of the other members. The governments of the individual countries don't miss out on anything, as the interest rates for their currencies (if they didn't use the euro) would probably be controlled by a central bank anyway. The problem, then, lies with the difficulty the ECB has in setting an interest rate that is suitable for all of the members of the euro area. There are 17 different members, with different economic and social structures, which can lead to a lack of convergence in their economic cycles (as discussed in the case study). Simplified, the lack of convergence means that while one country may be experiencing a period of economic boom, another country in the euro area may be in a recession. The "booming" country may want high interest rates in order to control the price level, while the country in recession would want exactly the opposite. This delicate balancing act is very difficult and is often criticised.
Also, as I have mentioned in previous posts, the euro area operates with a non-symmetrical inflation target which means that there is not the same emphasis put on increasing the inflation rate if it is too low, as there is on reducing it when it is too high. In my opinion this is a flaw in the system of the euro area, as it tends to lead to higher-than-necessary interest rates which does indeed lead to low price leves, but often at the cost of low economic growth and high unemployment.
Furthermore, certain signals that should be given off by changes in the exchange rate are often dampened in a monetary union the size of the euro area; one country's economic performance does little to affect the overall exchange rate of the euro. Ireland complained following their deep recession that, if they had their own currency, their large increases in AD would have led to high levels of appreciation of that currency and could have slowed down the level of export-led growth (as long as the demand for their exports was price elastic) and possibly helped give some early-warning signs to the government that a recession was on the horizon.