I will discuss studies of the mechanics and structure of metaphase chromosomes and nuclei extracted from mammalian cells using glass micropipettes. Using a combination of mechanical, biochemical and genetic approaches we have shown that the metaphase chromosome is a "chromatin gel", without a contiguous protein scaffold, and via SMC2 siRNA experiments, that condensin plays a major role as a "crosslinker". I will also discuss the "loop-extrusion" model for establishment of chromatid structure, with special attention to how it generates compaction of chromosomes along their length, or "lengthwise compaction", and how this provides a mechanism for chromatid and chromosome individualization. I will then describe use of the same general approach to analyze the mechanics of mammalian G1 nuclei. The nucleus shows two distinct mechanical responses: an initial chromatin-dominated elastic behavior, followed by a stiffer, lamin-dominated regime at larger extension. The low-force chromatin-based elasticity can be modulated by changing histone acetylation and methylation, and the morphology of the nucleus is impacted by these changes, with heterochromatinization driving the nucleus to be stiffer and rounder, and with euchromatinization destabilizing nuclear shape.