After being robbed in the USA in a Target parking lot in broad daylight, I now take precautions here at home that translate easily to travel. When I shop here, even for groceries, I have a very thin wallet in my pocket, with only one debit card and a little cash, drivers license, etc, and in the other pocket I have my cell phone and keys. I also use a small cross body shoulder bag with inexpensive essentials. If someone demands or takes my bag, they are welcome to it, its almost a decoy. 😏
I know that under usual everyday circumstances in the US pick pocketing is not that common (as opposed to being mugged or robbed), so my homeland strategy works well for me here, but I have witnessed it in Europe. A travel friend lost his pocket cash while being jostled getting on a Metro in Paris, and another traveler had her iPad snatched in a second.
While in Europe I always leave my large denomination stash, passport and extra credit card in the hotel safe. I take a medium size cross body tote with items I may need during my day out: lip balm, tissues, small or portions of a guidebook, small water bottle, map, etc. After I calculate what I will probably need for spending that day, I keep a small amount of cash, metro tickets etc in an accessible jeans or shirt/jacket pocket. I keep my stash cash and debit and credit cards in some type of zipped pouch, on my person. I bought a bra pouch (yes, bra) that attaches to the front strap and lies flat under my clothing. That's more comfortable for me than a money belt. I also have travel pants with pockets inside the waist, and there are other clothing items available online that have unobtrusive, zippered pockets almost everywhere, some are very clever! - and while not exactly cheap, these things can be a good travel investment if you travel frequently, I also use these pockets for my smartphone. It makes your day out so much more care free, nothing to "guard" or position the right way, or hold on to, wear on your chest, or worry about. I personally do not see the point of carrying an "anti theft" purse or bag: yes it may deter the experienced pickpockets, but if someone really wants to take the bag, it can still be snatched quickly and violently, so all of those "zipper locks" will be useless, and you are always "guarding" your bag. As others have said, it's also common sense, avoid being in the middle of a crowd if possible, and while traveling with luggage, never leave it alone, and take the good advice of others who have already weighed in here.
Traveling with children:
Years ago (BC - before cellphones 😊), while backpacking with my 11 year old son in Britain, I copied (reduced size) his passport as well as mine, our itinerary with all hostel/accommodation/personal contact information, and a $50 bill, all tucked neatly into a small, flat, tight plastic sleeve, which he wore inside his money belt under his clothes, and another one in his shoe! - just in case we were separated for some reason, he got distracted, darted off, and lost (as 11 yr old boys can do), etc. while nothing is guaranteed to work, in the unlikely event that we lost each other, he would have been able to go to a police officer, or at least hop in a cab and get to our hostel or BnB.
Carrying a bag/anti theft/cross body, and then worrying about possessions or money while traveling takes the joy out of it for me, therefore, my chosen style is the comfort of not having anything desirable to thieve or steal or pick, I carry it on my person, hidden and safe (or safe as can be...).
Happy and safe travels to all.