  Gravitational waves enable tests of general relativity in the highly
dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1
October 2019, we evaluate the consistency of the data with predictions from the
theory. We first establish that residuals from the best-fit waveform are
consistent with detector noise, and that the low- and high-frequency parts of
the signals are in agreement. We then consider parametrized modifications to
the waveform by varying post-Newtonian and phenomenological coefficients,
improving past constraints by factors of ${\sim}2$; we also find consistency
with Kerr black holes when we specifically target signatures of the
spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we
tighten constraints on Lorentz-violating coefficients by a factor of
${\sim}2.6$ and bound the mass of the graviton to $m_g \leq 1.76 \times
10^{-23} \mathrm{eV}/c^2$ with 90% credibility. We also analyze the properties
of the merger remnants by measuring ringdown frequencies and damping times,
constraining fractional deviations away from the Kerr frequency to $\delta
\hat{f}_{220} = 0.03^{+0.38}_{-0.35}$ for the fundamental quadrupolar mode, and
$\delta \hat{f}_{221} = 0.04^{+0.27}_{-0.32}$ for the first overtone;
additionally, we find no evidence for postmerger echoes. Finally, we determine
that our data are consistent with tensorial polarizations through a
template-independent method. When possible, we assess the validity of general
relativity based on collections of events analyzed jointly. We find no evidence
for new physics beyond general relativity, for black hole mimickers, or for any
unaccounted systematics.
