Over the last decade, memristive devices have been widely adopted in computing for various conventional and unconventional applications. While the integration density, memory property, and nonlinear characteristics have many benefits, reducing the energy consumption is limited by the resistive nature of the devices. Memcapacitors would address that limitation while still having all the benefits of memristors. Recent work has shown that with adjusted parameters during the fabrication process, a metal-oxide device can indeed exhibit a memcapacitive behavior. We introduce novel memcapacitive logic gates and memcapacitive crossbar classifiers as a proof of concept that such applications can outperform memristor-based architectures. The results illustrate that, compared to memristive logic gates, our memcapacitive gates consume about 7× less power. The memcapacitive crossbar classifier achieves similar classification performance but reduces the power consumption by a factor of about 1, 500× for the MNIST dataset and a factor of about 1, 000× for the CIFAR-10 dataset compared to a memristive crossbar. Our simulation results demonstrate that memcapacitive devices have great potential for both Boolean logic and analog low-power applications.