Most of these are TFA inhibitors, but there are some newer ones that target other things, such as ixekizumab (Taltz) and brodalumab (Siliq), both approved very recently.
Common to biologics is that they're all fairly new, so their long-time safety is not established. They are more precisely targeted than immune-system therapies such as methotrexate (a chemotherapy drug that also works on psoriasis), but they do interfere with your immune system in scary ways. There's evidence that they increase the risk of cancer as well as other diseases. Brodalumab has been associated with an elevated risk of suicidal ideation and behavior (!), so there's that.
All drugs can have negative effects, but in the end it comes down to what's the risk/reward ratio. If someone is in constant pain and barely can do anything it really doesn't matter if you die 5 or 20 years down the road to cancer when you get x years to live somewhat normal life. Life in extreme suffering can be worse than death. This is based on personal experience.
Humira etc is very expensive but works for lot of people that other drugs don't.
http://www.webmd.com/drugs/2/drug-3441/methotrexate-anti-rhe... https://en.wikipedia.org/wiki/Methotrexate
Some of the old ones are Humira and Enbrel, which have been out for quite a while (since 2000's). The newer ones are Cosentyx and Taltz, which has a higher cure rate. There are dozen of others that I don't remember. Just search for biologic for autoiummue. More drug companies are in the process of getting more drugs approved.