Investigating:
* "The police are looking into the robbery."
* "We're looking into the possibility of a new marketing strategy."
Considering:
* "I'm looking into buying a new car."
* "The company is looking into offering more flexible work arrangements."
Searching for information:
* "I'm looking into the history of this building."
* "She's looking into the best travel deals for her upcoming trip."
Considering a job or opportunity:
* "He's looking into several different job offers."
* "They're looking into expanding their business overseas."
The exact meaning of "looking into" will depend on the specific context and the other words used in the sentence.