Since none of us are able to read minds we can never truly know someone. On top of that people change over time, so the person you fell in love with may be someone entirely different today.
Even if you both love each other, times change and you might grow bored with the same old routine. This is the reason for most affairs, one spouse simply grows tired of the dull routine and wants to try something different.
While it is far from acceptable it is understandable and understanding is the first step to healing your marriage. While a lot of people would end their marriage after this act of betrayal, people often still love each other and might want to salvage their relationship even after this mistake.
But how can you trust them ever again after they back stabbed you like this? You swore to be faithful and they went off with someone else. Well there are certain things you can do to help mend the wound.
First of all, do not accept excuses. Just because you are willing to forgive and move forward does not mean you should just forget it and let them off the hook. They screwed up, big time, and they need to own up to their mistake for your relationship to work. If they want your relationship to work then they will do this, otherwise they may not be as serious as you are.
Another part of not accepting some half hearted apology is to remember the old saying "actions speak louder then words". If your spouse is truly sorry and wants to make amends, they will cut off all contact with the person they cheated with.
If they refuse to do this, or continue to see the person, then they probably are not as sorry as they led you to believe and you might want to simply cut your losses and move on with your life.
Also, do not belittle yourself. A lot of people blame themselves for their spouses affair, thinking they must have done something wrong to drive their partner to such lengths. Do not do this, it was their mistake not yours. If they had a problem they should have talked with you about it instead of running off into someone else's bed.
Lastly, whether you forgive them or move on, always hold your head high. You are not at fault for this and you deserve better. Whether you get that from your spouse or someone down the line is up to you. There is no law saying you have to stay with them if they refuse to change. Be understanding and cooperative, but never be a doormat.
As long as you try your best to make things work, and as long as your spouse realizes their mistake and tries as well, things will often work out in the end.