Most Christians will say the OT is there as a background story to help understand the NT better. They are kinda right in that it helps understand the NT better...but it is more than mere background.
In Exodus 19, God makes a covenant between Himself and the Israelites (the decendants of Jacob - who God renamed Israel). Unless you are an Israelite (or living in the Land of Israel), you are not part of the covenant. You can convert to Judaism and willingly accept the rules upon yourself and then your children will be bound to The Law due to being adopted into the Israelites.
The Law is an all or none deal - you cannot say part A applies but part B does not. This is where most Christians get it wrong. You can use The Law to show what God wants of Israelites, but that is it. You have to use other places to put rules onto everyone else.
For example, you can use the Cain and Abel instance to show God hates murder and that not doing it is applied to everyone. You can use the Council of Jerusalem to show that all Christians are to obstain from eating blood, eating meat given to idols, an from sexual immorality. To define what is in this immorality, you have to understand what those who said it would say - and they were all devout Jews. They would have put all the rules of The Law on sexual immorality into what is not allowed. So we can say those parts of The Law apply to Christians because of their ruling. It is not that we are referencing The Law and only applying parts of it to Christians, we are referencing the Council of Jerusalem and using those rules...some of which are based on The Law because they felt it was good to have everyone follow those parts (as told them by the Holy Spirit).
Also, most of the OT is not The Law, only a small portion of it is.