The two possible pathways toward artificial intelligence (AI)—(i) neuroscience-oriented neuromorphic computing [like spiking neural network (SNN)] and (ii) computer science driven machine learning (like deep learning) differ widely in their fundamental formalism and coding schemes ( Pei et al., 2019). Deviating from traditional deep learning approach of relying on neuronal models with static nonlinearities, SNNs attempt to capture brain-like features like computation using spikes. This holds the promise of improving the energy efficiency of the computing platforms. In order to achieve a much higher areal and energy efficiency compared to today’s hardware implementation of SNN, we need to go beyond the traditional route of relying on CMOS-based digital or mixed-signal neuronal circuits and segregation of computation and memory under the von Neumann architecture. Recently, ferroelectric field-effect transistors (FeFETs) are being explored as a promising alternative for building neuromorphic hardware by utilizing their non-volatile nature and rich polarization switching dynamics. In this work, we propose an all FeFET-based SNN hardware that allows low-power spike-based information processing and co-localized memory and computing (a.k.a. in-memory computing). We experimentally demonstrate the essential neuronal and synaptic dynamics in a 28 nm high-K metal gate FeFET technology. Furthermore, drawing inspiration from the traditional machine learning approach of optimizing a cost function to adjust the synaptic weights, we implement a surrogate gradient (SG) learning algorithm on our SNN platform that allows us to perform supervised learning on MNIST dataset. As such, we provide a pathway toward building energy-efficient neuromorphic hardware that can support traditional machine learning algorithms. Finally, we undertake synergistic device-algorithm co-design by accounting for the impacts of device-level variation (stochasticity) and limited bit precision of on-chip synaptic weights (available analog states) on the classification accuracy.