  We provide two families of algorithms to compute characteristic polynomials
of endomorphisms and norms of isogenies of Drinfeld modules. Our algorithms
work for Drinfeld modules of any rank, defined over any base curve. When the
base curve is $\mathbb P^1_{\mathbb F_q}$, we do a thorough study of the
complexity, demonstrating that our algorithms are, in many cases, the most
asymptotically performant. The first family of algorithms relies on the
correspondence between Drinfeld modules and Anderson motives, reducing the
computation to linear algebra over a polynomial ring. The second family,
available only for the Frobenius endomorphism, is based on a formula expressing
the characteristic polynomial of the Frobenius as a reduced norm in a central
simple algebra.
