Additive manufacturing, also called three-dimensional (3D) printing, is an emerging technology for printing net-shaped components layer by layer for applications in automotive, aerospace, biomedical and other industries. In addition to the vast design freedom offered by this approach, metal 3D printing via laser powder-bed fusion (L-PBF) involves large temperature gradients and rapid cooling and provides exciting opportunities for producing microstructures and mechanical properties beyond those achievable by conventional processing routes. Although these extreme printing conditions enable microstructural refinement to the nanoscale for achieving high strength. However, high-strength nanostructured alloys by laser additive manufacturing often suffer from limited ductility. Eutectic high-entropy alloys (EHEAs) represent a promising class of multi-principal element alloys that can form a complex hierarchical microstructure of dual-phase lamellar colonies and thus offer great potential for achieving excellent mechanical properties. Thus far, high-strength EHEAs are mostly fabricated viii through severe plastic deformation that usually results in highly textured nanostructures with strong plastic anisotropy, thus limiting their practical applications. In this work, we first harness the extreme printing conditions of L-PBF and favorable compositional effects of HEAs to produce a unique type of far-from-equilibrium microstructure in the form of dual-phase nanolamellae embedded in eutectic micro-colonies in an AlCoCrFeNi2.1 EHEA which exhibits an excellent combination of strength and ductility together with nearly isotropic mechanical behavior. Second, we apply the hierarchical, dual-phase nanostructure design motif to another EHEA of Ni40Co20Fe10Cr10Al18W2 to improve its mechanical properties. Compared to the prototype EHEA system of AlCoCrFeNi2.1, the compositional variations result in distinct diffusion and precipitation kinetics upon rapid solidification, which enables the activation of different deformation mechanisms. Third, we demonstrate that the highly tunable mechanical properties of AM AlCoCrFeNi2.1 EHEAs originate from the microstructural metastability implanted during L-PBF, which acts as profound embryos for a rich variety of microstructural evolution and phase transformations during post-printing heat treatment. We use a suite of state-of-the-art characterization and modeling tools to gain a fundamental understanding of the mechanistic origin of the tunable strength-ductility synergy of our AM EHEAs. In summary, the overall work aims to uncover the relationships of processing-structure-mechanical property-deformation mechanism in AM EHEA systems.