What countries today have severe restrictions against Christianity as state policy? What countries today have severe restrictions against Christianity as state policy? 
Is it possible to give a short overview with description of those policies? 

This source is quite good, however, it doesn't give precise wording of the state policy in a country, and in many countries on that list the persecution is more a result of clashes between clans rather then of the state policy. 

The top five countries listed there are: North Korea, Somalia, Iraq, Syria, and Afghanistan.
North Korea has severe restrictions against Christianity as state policy, with imprisonment and forced labour the penalty for even being a committed Christian, but not only Christians face persecution.  Margaret Stutley reports, in Shamanism that North Korean persecution of shamanism has caused the religion to go underground.

China has placed some restrictions on Christianity, including on the building of new churches, a restriction that has forced the existing churches visibly to overflow with worshippers on Sundays. The Vatican is not permitted to nominate bishops in China, so the official Catholic Church in China is somewhat disconnected from the worldwide Catholic Church. Both these policies, which have their origins in the humilities of the nineteenth century, have resulted in the development of underground churches. In spite of this, Christians can worship quite openly, as I have observed.  The greatest religious persecution is against the Falun Dafa, which is banned in China, with adherents subject to imprisonment and possible execution. 

Islam recognises Christians as "people of the book", so in Muslim-majority nations there tends not to be overt state restrictions on Christianity as a matter of policy, although more subtle persecution may exist, and in some countries there is hostility from the Muslim people. The World Watch List list the fifty countries where persecution of Christians is most rife, with most of them being Muslim-majority countries. Again, the existence of persecution is not always due to overt state policy but may be societal. For example, in Somalia, second on the World Watch List, the government is impotent, but grave danger exists in the form of the militant Islamist group al-Shabaab.