We compile and analyze ~200 trigonometric parallaxes and proper motions of molecular masers associated with very young high-mass stars. These measurements strongly suggest that the Milky Way is a four-arm spiral. Fitting log-periodic spirals to the locations of the masers, allows us to significantly expand our view of the structure of the Milky Way. We present an updated model for its spiral structure and incorporate it into our previously published parallax-based distance-estimation program for sources associated with spiral arms. Modeling the three-dimensional space motions yields estimates of the distance to the Galactic center, Ro = 8.15 +/- 0.15 kpc, the circular rotation speed at the Sun's position, To = 236 +/- 7 km/s, and the nature of the rotation curve. Our data strongly constrain the full circular velocity of the Sun, To + Vsun = 247 +/- 4 km/s, and its angular velocity, (To + Vsun)/Ro = 30.32 +/- 0.27 km/s/kpc. Transforming the measured space motions to a Galactocentric frame which rotates with the Galaxy, we find non-circular velocity components typically about 10 km/s. However, near the Galactic bar and in a portion of the Perseus arm, we find significantly larger non-circular motions. Young high-mass stars within 7 kpc of the Galactic center have a scale height of only 19 pc and, thus, are well suited to define the Galactic plane. We find that the orientation of the plane is consistent with the IAU-defined plane to within +/-0.1 deg., and that the Sun is offset toward the north Galactic pole by Zsun = 5.5 +/- 5.8 pc. Accounting for this offset places the central supermassive black hole, Sgr A*, in the midplane of the Galaxy. Using our improved Galactic parameters, we predict the Hulse-Taylor binary pulsar to be at a distance of 6.54 +/- 0.24 kpc, assuming its orbital decay from gravitational radiation follows general relativity.