This will vary by state law, but:
There are four general entry authorities for Peace Officers to make non-consensual entry into a residence:
1) Serving an arrest warrant (in my state it has to be a felony warrant), with reason to believe that the suspect is there. This would mean that this is the residence listed on his license, is the residence he gave at booking, or has been identified by a reliable means or source as the person's residence;
2) When serving a search warrant, and there are two distinct categories, "knock-and-announce," (the vast majority) and "no-knock." No-knock warrants must be specifically authorized by a judge, and lets keep it on track; that is another debate;
3) When in fresh pursuit of a violator, e.g., bad guy runs into your house;
4) Exigent circumstances that a person is at risk of serious bodily injury or death, e.g. a Disturbance call with people screaming inside, a 911 hang-up call with an extensive history of medical calls {this has been the vast majority of the ones I have done; fallen and can't get up, heart attacks, ODs, strokes, etc..}, or other facts and circumstances like reported gunfire inside of a house and so on.
When officers make entry under one of those circumstances, they are limited to making a "protective sweep" of the residence, a search for concealed persons who might represent a safety threat to officers. If they see contraband in plain view, they may seize it, but to go further than plain view, they must have consent, or they can hold the scene and get a search warrant )preferred). In my state, search warrants may be issued to search a residence for a wanted person as well, such as in cases of a misdemeanor fugitive who can't be apprehended by other means, though I haven't seen one yet.
In the case of the officer performing a "knock and talk," you really don't know what the officer is looking for. He may be there serving a misdemeanor warrant, he may be there on a felony warrant. He may be there on a disturbance call. What you present to the officer may in large part determine what the officer winds up doing.
Also, in most states, it is a violation to harbor a fugitive or hinder an arrest. Around here, if there is a person who has a felony warrant in your house, and you know that they are wanted, it is a felony for you to "conceal" them there. An example would be the "knock and talk" scenario. The officer says that they are looking for "John Doe." You say that Doe doesn't live here. The officer tells you that Doe gave this as his residence address two weeks ago. You say that Doe hasn't lived there in months. The officer will usually tell you that Doe has a warrant, and will ask you permission to search the house for Doe. You refuse. The officer tells you that:
a) Doe is a wanted felon,
b) you will be charged with a felony if they find Doe there,
c) They have the authority to, and will search the house, and they were just asking to be polite.
I have done that scenario many times. Sometimes Doe isn't there. Sometimes, the homeowner fesses up. Sometimes, we arrest Doe and the homeowner. Sometimes, Doe bolts out the back door, and if the cover guy back there is slow, we all get some exercise.
A good example of the evolving nature of exigent circumstances is a 911 hang up call I went to at abut 2 in the morning (all of the "good" stories happen at 2 in the morning). There was no history of calls at all the residence. There were no sounds of any disturbance at the residence.
The man who answered the door was extremely nervous. He claimed to be asleep, and said that he was alone. Hey, weird things do happen with telephones sometimes. But, I noticed that he did not appear to have just woken up; he was fully alert. He was also very nervous and kept looking over his shoulder, glancing back to the master bedroom. Then I heard a baby cry. I asked him again if there was anyone else in the house. Lying increases that articulable suspicion that something may be amiss (aside from the fact that 911 calls at 2 in the morning, in my experience, tend to be from a disturbance about 95% of the time).
Another voice (from a small child) cried out "Daddy, what's happening?" By this time, my second unit showed up. I asked for permission to check the house, but he refused. Okay, so what did this JBT do? Did I "respect" his rights, or did I exercise the authority that the courts say an officer has to make entry, under exigent circumstances. I made entry.
I found her in the bathroom. She was almost beaten to death, but that was making him too tired, so he fallen back to choking her, which required less physical effort. She made the 911 call, but he got the phone away from her quickly enough that all the call-taker heard was the line disconnecting. He had been beating her for hours, except when he assaulted her in other ways. If we would not have to decided to make an entry without consent, she would have died.
The point is, there are many ways for an officer to legally and Constitutionally make entry into a residence. When encountered with this, be polite. The officer is doing their job. If the officer is a prick, call IA. I would like to hear the rest of jrzy's story, now.