Degeneration of cognitive functioning due to dementia is among the most important health problems in the ageing population and society today. Alzheimerʼs disease (AD) is the most common cause of dementia, affecting more than 5 Mio. people in Europe with the global prevalence of AD predicted to quadruple to 106 Mio. by 2050. This chapter is focused on demonstrating models of neural circuitry and brain structures affected during neurodegeneration as a result of AD and how these model can be employed to better understand how changes in the physical basis in the electrochemical interactions at neuron/synapse level are revealed at the neural population level. The models are verified using known and observed neuropathalogical oscillations in AD. The thalamus plays a major role in generating many rhythmic brain oscillations yet, little is known about the role of the thalamus in neurodegeneration and whether or not thalamus atrophy is a primary or secondary phenomenon to hippocampal or neo cortical loss in AD. Neural mass models of thalamocortical networks are presented to investigate the role these networks have in the alterations of brain oscillation observed in AD. Whilst neural mass models offer many insights into thalamocortcial circuitry and rhythm generation in the brain, they are not suitable for elucidating changes synaptic processes and individual synaptic loss at the microscopic scale. There is significant evidence that AD is a synaptic disease. A model consisting of multiple Izhikevich type neurons elucidates now large scale networks of simple neurons can shed light on the relationship between synaptic/neuron degradation/loss and neural network oscillations. Focusing on thalamocortical circuitry may help explain oscillatory changes however the progression of AD is also usually associated with memory deficits, this implicates other brain structure such as the hippocampus. A hippocampal computational model that allows investigation of how the hippocampo-septal theta rhythms can bebe altered by beta-amyloid peptide (Aβ, a main marker of AD) is also described. In summary the chapter presents three different computational models of neural circuitry at different scales/brain regions and demonstrates how these models can be used to elucidate some of the vacuities in our knowledge of brain oscillations and how the symptoms associated with AD are manifested from the electrochemical interactions in neurobiology and neural populations.