  In this paper we present a detailed critical study of several recently
proposed non-Markovianity measures. We analyse their properties for single
qubit and two-qubit systems in both pure-dephasing and dissipative scenarios.
More specifically we investigate and compare their computability, their
physical meaning, their Markovian to non-Markovian crossover, and their
additivity properties with respect to the number of qubits. The bottom-up
approach that we pursue is aimed at identifying similarities and differences in
the behavior of non-Markovianity indicators in several paradigmatic open system
models. This in turn allows us to infer the leading traits of the variegated
phenomenon known as non-Markovian dynamics and, possibly, to grasp its physical
essence.
