I first encountered it as a young teenage Christian when I read the following words of Jesus found in Matthew 5 verse 20:
But more importantly than that, I knew that I was not up to that level of righteousness, and that bothered me, for unless I exceeded the Pharasaic righteousness I could not enter the kingdom of heaven. These were the plain words of Jesus, to be taken with full seriousness. What to do?
There are numerous ways to interpret and apply the Sermon on the Mount. One approach is to simply do your best to follow its regulations and hope you "pass the exam" so to speak. Jesus says don't be angry, so I'll try not to be angry. Jesus says don't lust, so I'll try my best to avoid women.
A second approach is to merely ignore it, which is perhaps an approach too often utilised by Christians.
Another approach is to read it as Jesus being the bearer of "New Law". This is perhaps the most popular approach in many evangelical circles. We read the Sermon on the Mount through Pauline eyes, where this Law that Jesus brings is a method of highlighting our need for the gospel. To use the language of Galatians, the Sermon on the Mount is our tutor which drives us to Christ.
There are a couple of fundamental problems with this popular approach however. The first is an obvious one: the apostle Paul didn't write the book of Matthew, and so to read this book through Pauline eyes is to do a disservice to the text, something which Richard Hays makes clear in his Moral vision of the New Testament. The second problem with this (dare I say Reformed) approach is the context the Sermon finds itself in. The Sermon on the Mount occupies Matthew 5-7. In chapter 4, right before launching into this extended discourse, Matthew gives us a summary of what Jesus is up to. He is preaching, teaching, and healing. What is He preaching about, what is He teaching about, what is He manifesting through healings? In short, the gospel of the kingdom. He's proclaiming, explaining and manifesting good news. Lets not forget that the Sermon on the Mount is found in the Gospel of Matthew. To slap a "Law" tag on what Jesus is saying and put it at odds with the gospel is a mistake in my opinion.
So where does that leave us? If we don't find here laws that we have to try our best to live up to or laws that are intended to weigh heavy on our conscience, what do we find? In a word, we find fulfillment. Fulfillment in what sense? I think there is dual fulfillment going on here: The primary fulfillment is Jesus as the Law incarnate. He says Himself that He did not come to do away with the Law but to fulfill it. Jesus is the embodiment of the Law. Where Israel failed, He succeeded. This is part of the reason why the crowds marveled once the sermon was finished. Jesus exhibited the authority which the scribes and Pharisees could only dream of: the authority to live out the Law. He spoke as one who knew the beauty of it, who knew the heart of it, and who knew the Law Giver, someone He could call 'Father'. Through word and deed, Jesus demonstrated the goodness of the Law.
The second fulfillment accomplished by Jesus is found (somewhat hidden) in the text following on from the Sermon on the Mount. That word "authority" mentioned at the end of chapter 7 plays a crucial function in the entire Gospel of Matthew, and so it should not surprise us to find it has a large role to play in how we interpret and apply the teachings of Jesus.
In chapters 8 and 9 especially we read of Jesus' authority extending to the lives of those around Him. A leper says to Jesus, "You can make me clean", and Jesus does so. A centurion urges Him to "only speak a word, and my servant will be healed", realising that Jesus is a man with the authority to accomplish what He says. We see this authority in action again when wind and waves are stilled by His voice.
In the light of this authority, the message of the Sermon on the Mount is shockingly good news. Jesus has the power to fulfill the Law in us. Having died and rose again, He says at the end of Matthew's account, "All authority in heaven and earth has been given to me". He doesn't say this in a merely commanding way, but in a relational way, promising to be with us always. The wonderful news is that the authority of Jesus is something which is for our benefit. It is an authority which authorises, an authority which empowers.
The Sermon on the Mount is the description of a life lived under the empowering authority of Jesus. In the middle of Matthew's Gospel, Jesus says to the Pharisees,"If I cast out demons by the Spirit of God then the kingdom of God has come upon you". He could say something similar with regards the Sermon on the Mount: "If I transform the unrighteous into the righteous by the Spirit of God then the kingdom of God has come upon you".