Monitoring your IP is worth looking at it with respect to the multiple types of IP that exist - trademarks, copyrights, trade secrets and confidential information, and patents.
Copyrights are fairly straightforward with respect to monitoring and protects what we call work of authorship.
Trademarks are your brand. What you’re looking for are other companies, third parties, especially competitors, that are using a mark that is similar to yours.
Trade secrets and confidential information are interesting when it comes to monitoring, because as opposed to other types of intellectual property where you’re looking at what other comapany's are doing publicly, you're getting a little bit more personal.
Patents can be a littly tricky because as opposed to trademarks, where you can look at the brand and see similarities between yours and someone else’s, patents have claims that describe the legal bounds of what it protects.