  During these last decades, our knowledge of evolutionary and structural
properties of stars of different mass and chemical composition is significantly
improved. This result has been achieved as a consequence of our improved
capability in understanding and describing the physical behavior of matter in
the different thermal regimes characteristic of the various stellar mass ranges
and evolutionary stages. This notwithstanding, current generation of stellar
models is still affected by significant and, usually, not negligible
uncertainties. These uncertainties are related to our poor knowledge of some
physical proceses occurring in the real stars such as, for instance, some
thermodynamical processes, nuclear reaction rates, as well as the efficiency of
mixing processes. These drawbacks of stellar models have to be properly taken
into account when comparing theory with observations in order to derive
relevant information about the properties of both resolved and unresolved
stellar populations. On the other hand, observations of both field and cluster
stars can provide fundamental benchmarks for constraining the reliability and
accuracy of the theoretical framework. In the following we review some
important evolutionary and structural properties of very-low and low-mass
stars, as well as the most important uncertainties affecting the stellar models
for such stars. We show what are the main sources of uncertainty along the main
evolutionary stages, and discuss the present level of agreement between theory
and observations.
