[glatt]

Work began to recreate her in 2002, using traditional materials and craftsmanship employed during the 18th Century.

The recreation used over 50km of planks, 70,000 hand-forged nails, 10,000 bolts, 1,000 rigging blocks and 10 cast iron cannons.

I was wondering how it was navigating the Thames with sails down. I figured it must have engines, and wasn't quite the historical replica they made it out to be.

According to Wikipedia:

One small change was that the headroom of the deck was increased by 10 cm, since today's seamen are taller than their ancestors.[24]

While the exterior remains true to the original, the interior is highly modern. The ship has an electrical system and propellers powered by diesel engines.
...
Other enhancements include satellite navigation, communications equipment, modern facilities for the crew (kitchen, lavatories, washing machines, desalination equipment, ventilation, refrigerators), watertight bulkheads and fire protection (fire sprinkler systems, fire hydrants etc.). Most of this new technology was necessary to pass national and international safety regulations.