Technically speaking, the frequencies between 1.8 and 30 MHz are considered short wave. Radio signals within this range can "bounce" off the ionosphere and can therefore be received at a much greater distance than other freqencies.
When I first started to listen, it seemed like I had discovered another Internet. There are many times of transmissions. I often hear music broadcasts from South America and Asian talk shows. There are also many government news broadcasts (BBC, Radio Australia, Radio China International, Radio Havana), the occasional pirate, numbers stations, and coded military transmissions.
I mainly look for pirates and things that seem mysterious. It's fun to hear the static give way to something done by a person, even if it turns out that it's just a radar.
It is possible to spend a lot of money on radio equipment, but I have not done that. Here is the radio I use the most: