  $\phi$CDM models provide an alternative to the standard $\Lambda$CDM
paradigm, while being physically better motivated. These models lead to a
time-dependent speed of sound for dark energy that is difficult to replicate by
$w$CDM parametrizations. We review the most up-to-date status of observational
evidence for the $\phi$CDM models in this paper. We start with an overview of
the motivation behind these classes of models, the basic mathematical
formalism, and the different classes of models. We then present a compilation
of recent results of applying different observational probes to constraining
$\phi$CDM model parameters. Over the last twenty years, the precision of
observational data has increased immensely, leading to ever tighter
constraints. A combination of the recent measurements favors the spatially flat
$\Lambda$CDM model, but a large class of $\phi$CDM models is still not ruled
out.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology