Current situation in Europe

Bulgaria: There is evidence of under-age girls being forced to marry under sharia law[9] and of forced conversions[10].
France: We found no evidence of the existence of sharia courts. 
Germany: Controversial decisions include lowering of murder charges to manslaughter and authorities turning a blind eye in cases of ‘honour’ killings[11].
A Frankfurt judge refused a divorce to a German Muslim woman who, despite the violence she was subjected to not being in dispute, was forced to remain married[12].
Netherlands: The practice of conflict resolution based on sharia does not have the status of arbitration, since Dutch law does not allow for arbitration for such (family law) subjects as respondents indicate to be subject to conflict resolution. A study carried out in Nijmegen found that that Islamic arbitration is happening but concluded that there are no sharia courts[13].
Norway: Norwegian Foreign Minister Store stated that sharia councils or courts are “out of the question”. There is no evidence of any courts/tribunals existing (officially) in any Scandinavian country. In
Spain: A Muslim woman was kidnapped and ‘tried’ in a makeshift sharia ‘court’ sentenced to death by stoning for adultery but managed to escape.  The men in charge of this ‘court’ were arrested but freed because the woman did not appear in court[14].
Sweden: Muslim groups are reported have asked to “apply Islamic inheritance, marriage and divorce laws”[15].
: Although only 2.8%
[16] of the population are Muslim, sharia is a greater problem there than it appears to be in the rest of the EU (with the possible exception of Bulgaria).  From the limited information available, it would appear that the UK is the only major European country where sharia is practised on any scale, and it has some indirect support from the secular legal system. While sharia is not recognised directly in British law, sharia decisions can be treated as arbitration, with the decisions, particularly financial ones, enforceable by the secular courts. Muslim Arbitration Tribunals (MATs) operate under these powers conferred by the Arbitration Act. Their website shows [17] they are seeking to appear to be an official judicial agency, and questions have been raised about whether their sphere of activity is expanding into family matters, which would be impermissible. Arbitration is an Alternative Dispute Resolution process conducted by an abitrator agreed by the parties operating under rules agreed by them in advance.  Trial before a judge with the power to enforce a ruling through the civil courts should not be confused with mediation, which seeks to find an agreement between parties. MATs are not statutory tribunals and have no legal status.
The fact that so many sharia rulings in Britain relate to cases concerning divorce and custody of children is of particular concern, as women are not equal in sharia law, which also contains no specific commitment to the best interests of the child that is fundamental to family law in the UK.

Many women believe that such arbitration decisions are legally binding on them. There is pressure on women from within their communities to submit to the MAT for determination of family or inheritance disputes rather than using legitimate courts. It is thought that many women are reluctant to challenge the decision of a MAT in a court, therefore even though the decision of the MAT is in fact unenforceable, women are still deprived of their right to equality at law.
There is an assumption that those who attend sharia courts do so voluntarily and that unfair decisions can be challenged. Since much of sharia law is contrary to British law and public policy, in theory they would be unlikely to be upheld in a British court. In reality, women are often pressured by their families into going to these courts and adhering to unfair decisions and may lack knowledge of their rights under British law. Moreover, refusal to settle a dispute in a sharia court could lead to threats, intimidation or isolation[18].
In the UK, the law relating to failure to register marriages, to female genital mutilation and forced marriages exists but is rarely if ever the subject of prosecutions.
More information here[19].

(Please also see items 3, 4 and 5 on the Further Reading list below.)