I would recommend to take a look at the website of Meditation and Mindfulness Research Group at Liverpool John Moores University. They not only present the results of various studies but also explain those in simpler, not-too-scientific terms. In their research blog they discuss neuroplasticity and meditation, neural mechanisms of attentional control in mindfulness meditation or Cognition and Emotion in Meditation, to name a few.
This article also seems to nicely sum up the effects of meditation with links to the peer-reviewed articles. The author groups the effects of meditation in the following categories:
- It boosts your health
- It boosts your happiness
- It boosts your social life
- It boosts your self-control
- It changes your brain (for better)
- It improves your productivity
- It makes you wiser
On the other hand, there are also claims that there are serious drawbacks of mindfulness meditation. Mind focusing is seen as an opposite of mind wandering which tends to stimulate one's creativity. Thus, it is claimed that too focused mind can lead to decreased creativity. Another drawback is related to decreased ability to perform implicit learning:
implicit learning - the kind that underlies all sorts of acquired skills and habits but that occurs without conscious awareness. In the study, participants were shown a long sequence of items and repeatedly challenged to guess which one would come next. Although supposedly random, it contained a hidden pattern that made some items more likely to appear than others. The more mindful participants were worse at intuiting the correct answers (...)
Interestingly, here you can see the response of another scientist who researches mindfulness meditation who, in short, does not agree with the drawbacks mentioned above.
In general, the research on meditation started only recently and it is too early to state any definite answers. There are also signals that the methodology of most of the studies is flawed and much more funds and trials are needed to obtain more reliable results.