This work is a first step towards a long-term goal of understanding computations occurring in the brain and using those principles to make more efficient machines. The traditional computing paradigm calls for using digital supercomputers to simulate large scale brain-like neural networks resulting in large power consumption which limits scalability or model detail. For example, IBM's digital simulation of a cat brain with simplistic neurons and synapses consumes power equivalent to that of a thousand houses! Instead of digital methods, this work uses analog processing concepts to develop scalable, low-power silicon models of neurons which have been shown to be around ten thousand times more power efficient. This has been achieved by modeling the dynamical behavior of Hodgkin-Huxley (H-H) or Morris-Lecar type equations instead of modeling the exact equations themselves. In particular, the two silicon neuron designs described exhibit a Hopf and a saddle-node bifurcation. Conditions for the bifurcations allow the identification of correct biasing regimes for the neurons. Also, since the hardware neurons compute in real time, they can be used for dynamic clamp protocols in addition to computational experiments. To empower this analog implementation with the flexibility of a digital simulation, a family of field programmable analog array (FPAA) architectures have been developed in 0.35 um CMOS that provide reconfigurability in the network of neurons as well as tunability of individual neuron parameters. This programmability is obtained using floating-gate (FG) transistors. The neurons are organized in blocks called computational analog blocks (CAB) which are embedded in a programmable switch matrix. An unique feature of the architecture is that the switches, being FG elements, can be used also for computation leading to more than 50,000 analog parameters in 9 sq. mm. Several neural systems including central pattern generators and coincidence detectors are demonstrated. Also, a separate chip that is capable of implementing signal processing algorithms has been designed by modifying the CAB elements to include transconductors, multipliers etc. Several systems including an AM demodulator and a speech processor are presented. An important contribution of this work is developing an architecture for programming the FG elements over a wide dynamic range of currents. An adaptive logarithmic transimpedance amplifier is used for this purpose. This design provides a general solution for wide dynamic range current measurement with a low power dissipation and has been used in imaging chips too. A new generation of integrated circuits have also been designed that are 25 sq. mm in area and contain several new features including adaptive synapses and support for smart sensors. These designs and the previous ones should allow prototyping and rapid development of several neurally inspired systems and pave the path for the design of larger and more complex brain like adaptive neural networks.