An ordered differential field (ODF) is a an ordered field $(K,\leq)$ equipped with a derivation $\delta:K\to K$; no interaction of $\leq $ and $\delta$ is assumed. A closed ordered differential field (CODF) is an existentially closed ODF. M. Singer has shown that CODFs are axiomatizable and constitute the model completion with quantifier elimination of ODFs in the first order language $\{+,-,\cdot,\leq,0,1,\delta\}$.

Recently some progress was made in the model theoretic study of CODFs and I will review this (after presenting CODF in a geometric way). A central theme in the talk will be an intermediate value theorem for continuous semi-algebraic functions in the CODF context.