PSR J2032+4127 is a 143-ms gamma-ray pulsar recently found to be in a long period (45-50 year) and highly eccentric orbit with the massive Be star MT91 213. An extensive observing campaign with VERITAS, MAGIC and Swift-XRT was conducted over the fall 2017 periastron passage, resulting in the detection of TeV gamma-ray emission from the location of the binary. The detection of this gamma-ray binary makes it only the second such system with a pulsar established as the compact object. We present 100 hours of detailed observations across the periastron passage, which reveal that the TeV flux varied by an order of magnitude over timescales of days. Strong X-ray variability was also observed, but the X-ray and TeV variability are not directly correlated. We compare these observations with existing models of the system, concluding that significant revisions are required. We further discuss the presence of the steady and extended TeV source TeV J2032+4130, which lies in the same direction as PSR J2032+4127, and its potential association with the pulsar.