As a few of us are working our way through the laws in Exodus, it may raise the question - do they apply today, and if not, then why are we reading them!
Dr. Jim Hamilton tackles this question in this 10 minute summary. First, we must understand that Jesus initiates a new covenant in his blood (Mk 14:24). Since we are under the new covenant, and not the Mosaic covenant, we find the usefulness of the old in Romans 15:4 -
For whatever was written in former days was written for our instruction, that through endurance and through the encouragement of the Scriptures we might have hope.
So, Exodus and Deuteronomy were written for our good! We are not bound by the details of a law that was written to a particular people in a particular place at a particular time for a particular purpose. We cannot, either, throw it out of the window! We must learn from it!
For all who have sinned without the law will also perish without the law, and all who have sinned under the law will be judged by the law. Romans 2:12
... for sin indeed was in the world before the law was given, but sin is not counted where there is no law. Romans 5:13
So, before and after the Mosaic covenant - there is sin. Where there is sin, there is punishment. There is redemption from sin through the sacrifice of Jesus. One helpful axiom I have heard is to observe the New Testament carefully and learn from the definitions of sin that you see there.
The 10 minutes you spend in this video will certainly help you understand how to apply those law-passages in the Old Testament.