Advancements in electronics and energy storage and conversion technologies brings with it myriads of exciting material design challenges. Charge-containing block polymers (BPs) offer unique features which can overcome some of these challenges and have thus aroused substantial interest within the field of designer soft materials. The properties of BPs are intricately coupled to the dynamic and rich nature of the nanostructured assemblies, which result from the phase separation between blocks. The introduction of strong secondary forces, such as electrostatics and hydrogen bonding (H-bonding), into BPs greatly influences their self-assembly behavior, and therefore affects their physical and electrochemical properties often in nontrivial ways. In this review, some of the prevailing research, which has expanded the understanding of structure-property relationships to include several design strategies for improving ionic conductivity and modulus in charged block polymers, is presented. The profound extent to which electrostatics and hydrogen bonding impact block polymer thermodynamics, an extent which is demonstrated by recent theoretical and experimental work, is also highlight. Insights gained from the research presented here help to lay the groundwork for a long and bright future in the field of advanced soft materials.