the tldr answer: SVMs are theoretically powerful but either impractical or pointless.

The longer answer:

SVMs comes with two theoretical benefits: 1. A guaranteed optimal solution. You get this with simpler techniques like logistic regression. 2. The ability to use non-linear kernels, which can offer much more power than logistic regression (on par with neural networks).

So, at first, it seemed like SVMs were the best of all worlds, and a lot of people got excited. In practice, though, non-linear kernels slowed training down to the point of being impractical. Linear kernels were fast enough, but removed the second benefit, so most people would prefer to use established linear techniques like logistic regression.