Technically, a tariff is a tax on imports, that is paid by the importer of the goods subject to a tariff. Although precisely where the economic incidence of tariffs fall is up for debate. i.e. If the importers are able to pass on the cost of the tariff to somebody else, then it is not really them that the burden of the tariff falls. But where this burden falls might have a significant impact on whether you think tariffs are a good idea or not.
Historically, the USA funded the federal government largely through tariffs, back in the days when there was no federal income tax. Since the 30's this has changed and tariffs have largely fallen away in favour of other tax raising methods until now, where some might say America is returning to it's historic norm.
So what are the benefits and costs of tariffs and how does this vary over time?
Personally, being of a libertarian leaning, free market advocate, I have not been in favour of them and see them as a bad idea. The division of labour across the globe has lead to specialization and higher productivity on a global level although one must recognise that there has been localised negative effects on areas that now find themselves bereft of traditional industries. David Ricardo's theory of comparative advantage makes the argument why each country is better off specialising and only producing the things it is best at rather than trying to produce everything itself.
But I've heard criticism of this argument along the lines of the fact that it makes no consideration of future possible comparative advantage. i.e. Taiwan didn't start off in the 70's with a comparative advantage for producing microchips. It was a deliberate (industrial) policy to develop this industry that it eventually developed a comparative advantage for. It didn't just stick to it's existing comparative advantage in rice and fishing. So perhaps tariffs are needed to help protect certain industries while they develop?
This is know as the "infant industry" argument. Protect developing industries against established global competitors with tariffs (and perhaps subsidies) until they have developed enough to compete. But even if this is true, it doesn't completely undermine Ricado's argument. We are still better off specializing and not trying to produce everything for ourselves.
Are trade deficits inherently bad? It seems to me that Trump believes that the very existence of a trade deficit is bad, evidence of a country "ripping off" the US. But is that always the case? Not all industries can be re-located to inside the USA. Madagascar for instance exports a lot of vanilla to the USA. That can't be grown in the US so has to be imported. They are also so poor that they can hardly afford to buy anything the US makes. It is hard to characterise them as "ripping off" the US just because they have a trade deficit.
Will tariffs help bring back industry that has moved abroad to exploit cheaper labour? Will it lead to higher prices for consumers or might that only be in the short term? And if other countries retaliate, will that negate the benefits, leading to everybody becoming worse off?