A crossover study has the advantage over a simple double-blind study that the variability between patients is minimized because each patient crossing over in effect serves as their own control. One disadvantage is that long term effects cannot be tracked with this approach. Another disadvantage is that curative therapies cannot be tested after one another or before a placebo.
There are some important issues with respect to the design of cross-over studies. Two in particular may often crop up.
First is the issue of order effects, because it is possible that the order in which treatments are administered may affect the outcome. An example might be a drug with many adverse effects given first, making patients taking a second, less harmful medicine, more sensitive to any adverse effect.
Second is the issue of carry-over between treatments. In practice carry-over can be and is often dealt with by the use of a wash-out period between treatments, or by making observations sufficiently later after the start of a treatment period that any carry-over effect is minimized.