The important advances in modern NLP are being made using neural networks. Specifically, recurrent neural networks (and sometimes convolutional neural networks) are consistently being demonstrated to replace decades of heuristics using representations learned entirely from data (identical advances are being made in computer vision). This is important because it's essentially impossible to enumerate all the subtleties inherent in language(s), and bespoke models will be naturally fragile as a result.

Some of the more interesting examples of neural network & NN-inspired approaches to NLP include:
Question Answering [1, 2]

Sentiment Analysis [3]

Machine Translation [4]

Text Classification [5]

Natural Language Summarization [6]

etc. etc.

Some of the key players in the field include Richard Socher, Chris Manning, Quoc Le, Tomas Mikolov, Andrej Karpathy, David Blei, Jason Weston, Ronan Collobert, etc. This is a highly incomplete list, but if you use Google Scholar or visit their respective homepages you'll find loads of great material.

If (quite reasonably) you find the academic literature a bit imposing, I encourage you to explore the fundamentals by working through:

Andrew Ng's Coursera Machine Learning Course
https://www.coursera.org/learn/machine-learning

Google's Deep Learning (Tensorflow) Course @ Udacity
https://www.udacity.com/course/deep-learning--ud730

Chapters 1-5 of Introduction to Statistical Learning
http://www.stat.berkeley.edu/~rabbee/s154/ISLR_First_Printin...

Part II of Yoshua Bengio's Deep Learning Book
http://www.deeplearningbook.org/

& finally Richard Socher's excellent NLP course @ Stanford
http://cs224d.stanford.edu/

https://www.youtube.com/watch?v=sU_Yu_USrNc&list=PL_6hBtWGKk... (all lectures)

It feels like a lot of material, and it is, but it's important to understand the foundation to do meaningful, flexible work. If you spend a week bringing a black box stack online and the machine does not produce a satisfyingly magical result you'll find yourself grasping at straws in the absence of strong fundamentals.

Some additional resources that are fantastic include Colah's blog (http://colah.github.io/), specifically the pieces on Representations & LSTMs (but all of it really), as well as Andrej Karpathy's piece on 'The Unreasonable Effectiveness of RNN's (http://karpathy.github.io/2015/05/21/rnn-effectiveness/).

Some other touchstones include:

http://www.wildml.com/2015/11/understanding-convolutional-ne...

http://www.wildml.com/2016/08/rnns-in-tensorflow-a-practical...

https://www.youtube.com/watch?v=xK-bzjIQkmM&list=PL5bqIc6Xop... (Yoshua Bengio on RNNs)

https://www.youtube.com/watch?v=eyovmAtoUx0 (Bay Area Deep Learning School)

https://www.youtube.com/watch?v=s63vOy1kvsU&list=PLlJy-eBtNF... (Jeff Dean of Google Brain)

Some of the key computing frameworks you might use include those listed in the comments here, specifically Pandas, Scikit, NLTK and Stanford CoreNLP. Additionally, TensorFlow has great tutorial material, and the Keras framework (https://keras.io/) makes it wonderfully straightforward to build complex neural network models.

Also, lean hard into good, well-studied training data, including SQuAD, IMDB, the Penn Treebank.

https://rajpurkar.github.io/SQuAD-explorer/

http://ai.stanford.edu/~amaas/data/sentiment/

http://www.cis.upenn.edu/~treebank/home.html

Better yet, create your own data -- find a problem space that's fundamentally fascinating (I love cooking) and get after it. Scrape together the information you need to create the problem you've always wanted to solve.

Best of luck!

[1] https://cs.umd.edu/~miyyer/pubs/2014_qb_rnn.pdf

[2] https://arxiv.org/abs/1506.07285

[3] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.383...

[4] http://cs224d.stanford.edu/papers/seq2seq.pdf

[5] https://research.facebook.com/blog/fasttext/

[6] https://arxiv.org/pdf/1509.00685v2.pdf