Over the last decades, the digital revolution has continuously increased the demand for more computational power. However, with the exponential rise of artificial intelligence applications in virtually every aspect of today's life, these additional demands can not be met by relying on the already decreasing Moore's law scaling of classical transistor technology. To overcome these limitations, novel computation schemes are being explored to meet the needs of the rising AI industry by transferring brain-inspired algorithm concepts into direct hardware implementations. Such concepts, often referred to as neuromorphic computing, not only demand a new bottom-up architecture design but also advanced memory and information processing devices. Promising candidates for novel in-memory elements are memristors, which resistance is based on previous signals, functioning similarly to synapses in the human brain. Implementing such plastic, history-dependent properties into single nanoelectronic elements is a promising approach to address the need for advanced functionalities. One pathway includes the integration of new material systems like ferroelectric or phase change materials offering fundamentally new properties at the nanoscale. This thesis explores the unique potential of ferroelectric domain walls for enabling advanced functionalities and developing novel memristive devices. In this work, the properties of conductive domain walls in archetypical ferroelectric Pb(Zr,Ti)O3 thin films are studied with the goal of exploiting the conductive domain wall-channels for devices with memristive functionalities. Detailed studies on the growth conditions of highly tetragonal PZT films on DyScO3 substrates were carried out, leading to reliable methods for creating PZT films with both pristine and artificially created conductive domain walls. Within the thesis, the first observations of highly conductive normally neutral 180° domain walls are reported. A combination of studies, including high-resolution AFM-based techniques such as PFM and cAFM, temperature dependent measurements and cryogenic current transport experiments together with phase-field simulations as well as STEM-cross section analysis, revealed the complex and distorted structure of the thought-to-be straight 180° domain walls. The explored intrinsic conduction mechanism is facilitated by charged domain interfaces created through the interaction of the ferroelectric and ferroelastic domain boundaries. The integration of graphene electrodes allowed the stabilization of multi-domain states in the fabricated Gr/PZT/SRO capacitors enabling the confinement of the highly conductive domain walls inside the device area. Memristive functionalities are achieved by gradual altering of the created mixed-domain states through electrical stimuli. A different approach to control and stabilize domain walls for device applications is demonstrated by the introduction of high-resistive platinum electrodes. The finite resistivity of the electrodes enabled a controlled switching of individual domains and the precise positioning of the 180°-domain walls. The combination of these techniques resulted in fully symmetric and linear memristive properties and the development of the first proximity-sensitive domain wall memristor.