Heating with wood both has and hasn't changed much over the last 100 years. The simple wood stove is being replaced with higher efficiency catalytic, pellet stoves and masonary furnaces which give off much much less smoke than earlier stoves.
Pellet stoves burn small fuel pellets that look a bit like rabbit feed but are made from waste compressed sawdust. Pellet stoves have augers than continusouly feed fuel into the small combustion chamber where a high airflow burns the fuel at a very high temperature. A fan blows over the burning chamber to quickly moves the heat into the room. They usually have a "low-med-hi" setting which controls how often the augers feed fuel into the burn chamber. These are very efficient, there is almost no smoke and the fuel is cheap - $4.50 a 40lb bag which lasts about a day in a 3000sq ft house. At this time of writing the fuel is about 5x cheaper than oil for the same amount of heat but unlike logs is clean and convenient. In Europe truck deliber bulk fuel pellets bu the ton thorugh a giant hose into a bin. Pro: cheap to run, heats up quiclkly, almost no smoke, simple chimney. Con: expensive to buy, not silent, require electricity to run.
Masonry furnaces came out of Europe and Russian a century ago and are only now gaining any form of popularity. The idea is to burn a load of fuel (say 50 pounds of wood) very very quickly at a high temperature where it's most efficient and smoke free and have this heat up 10 tons of stone. Essentially a large brick or stone sealed fireplace the stonework is to accomidate the exhaust gases as they take a convoluted path up and down giving off their heat to the tons of stone as they pass by. These stoves, which are really furnaces, burn only for an hour or two. The stone absorbs all the heat, never gets too hot to the touch but gives off heat all day. On the absolute coldest days you might need to burn it twice, although typically once in the morning is good enough. Pro: very very clean and efficient. Needs no electricity. Can heat hot water and have a bake overn chamber. Silent. CON: big and expensive. All custom built and built in. Chimney non-trivial. Takes a while to heat a room up.
The wood stove has been steadily improved over the ages. It can be a small source of heat - a heater - or it can be a wood burning cook stove wood burning furnace. The outdoor furnace type are the smokiest type known - it's part of their design. None of these are particularly clean though.
The is your old fashioned open hearth fireplace. The good news is that it works. The bad news is that it wastes a lot of heat. Open fires make some poeple nervous and you can't really have the fire going while you're away. More for aesthetics than as a primary heat source. A well cleaned chimney and a good fire won't pollute much.