I'm in the process of buying a fixer upper and I know demo will be a huge process. I've talked to a few investors who are demoing houses that say they don't always get permits. They said depending on the part of the city and whether its monitored by city permit people depends on if they'll get the permit. Obviously they're taking the chance here and hoping they won't get caught. What happens if you do get caught? This seems like if you get caught you're screwed and will have to pay a bunch of fines.  How could they get the dumpster and not be found out since the dumpster is a dead giveaway theres reno going on inside that needs a permit? Hide the dumpster and hope no nosy neighbors spot it? They also said they try to hide the work going on as much as possible and avoid permits when they can as the city is strict on who can perform the work, as they have to be licensed and insured. I'm thinking the crews they use are not. Wouldn't this cause problems down the road when you go to sell the house and it looks completely different than previously or would nobody know? 

@Danielle Scott

Permits are required for most projects.  Usually you get caught because a neighbor complains.  The dumpster is definitely a give away.  It can be a big hassle to get through the permit process and the requirement for licensed contractors will cost more money.  Fines and work stoppage will occur if you get caught.  It’s not a good start if you plan on doing multiple projects in a city.  Having that reputation will not benefit you with the city.  You could have a problem if a fire occurs during rehab with no permit.  The insurance claim could be denied.

You should pull a permit.  Remember there was a big problem with the HGTV show Windy City Rehab for not pulling permits, getting caught and going beyond there approvals.  If you borrow money and get shut down for 30-90 days what does that do to your budget.

I couldn't have said it better than @Kenneth Garrett - get the permit. It might be more of a hassle up front, but it will protect you from a lot of potential fines and issues if you get caught without a permit. I'd rather be safe than sorry in these situations, especially when it involves demoing.

Is this an entire gut job type rehab or are you doing cosmetic type upgrades? 

If you are gutting get the permit. If only cosmetic upgrades I usually don’t.