They're the perfect blend of theoretically elegant and practically impractical. Training scales as O(n^3), serialized models are heavyweight, prediction is slow. They're like Gaussian Processes, except warped and without any principled way of choosing the kernel function. Applying them to structured data (mix of categorical & continuous features, missing values) is difficult. The hyperparameters are non-intuitive and tuning them is a black art.
GBMs/Random Forests are a better default choice, and far more performant. Even simpler than that, linear models & generalized linear models are my go-to most of the time. And if you genuinely need the extra predictiveness, deep learning seems like better bang for your buck right now. Fast.ai is a good resource if that's interesting to you.