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.

Have been in the industry for quite a while, and I think one of the often-overlooked non-technical reasons is they are hard to get an intuitive feel of, compared to ANNs. This might seem irrelevant, but think about it - someone who doesn't have a degree/rigorous training in ML or a ML heavy program (and this population is big in the industry, people who are looking to get into ML, from say analytics or software dev) will try out things he/she can identify with. ANNs are positioned exactly right for this - they're sufficiently sophisticated, you can quickly get a high-level idea, and there is the attractive comparison to how our mind works. So that's what people try out early amongst advanced algos. The industry doesn't give you a lot of time to explore, so once you have invested time to pick up ANNs, you tend to hold on to the knowledge.

I've also conducted multiple training sessions/discussions with small groups on ML, and it supports what I've said. SVMs are hard to explain to a general crowd; with ANNs I've enough visual cues to get them started. Sure, they mightn't get the math right away, but they understand enough to be comfortable using a library.

As an aside, a comment here mentions Logistic/linear regression dominates the industry. I think it is for a similar reason. They're simple to understand and try out. That doesn't make them good models, in my experience, on a bunch of real-world problems.

Now if you ask me about the technical cons of SVMs, I'd say - scalability of non-linear kernels and the fact that I've to cherry-pick kernels. Linear and RBF kernels work well on most problems, but even then, for a bunch of problems where RBF seems to work well, the number of support vectors stored by the model can be massive. If I weren't to be pedantic about it and excuse the fact that the kernel seems to be "memorizing" more than "learning", this is still a beast to run in real time. nu-SVMs address this issue to an extent, but then we are back to picking the right kernel for the task. This is one thing I love about ANNs - the kernel (or what essentially is the kernel) is learned.

Also, hyperparameter optimization is a bit painful. Zoubin Ghahramani of Cambridge is a champion for Gaussian process models which are as flexible as SVM/SVC, but have more disciplined approach: via well-chosen priors (Bayesian structure) and single-step hyperparameter optimization.

1.SVM is not interpretable just as DL.

2.Hard to parallel if you're using kernels other than linear one.

3.So-so performance.

They tend to create difficult to interpret models that don't perform as well as other "black box" modeling methods (GBMs, neural nets, etc.)