  Spiking neural networks (SNN) are a biologically inspired model of neural
networks with certain brain-like properties. In the past few decades, this
model has received increasing attention in computer science community, owing
also to the successful phenomenon of deep learning. In SNN, communication
between neurons takes place through the spikes and spike trains. This
differentiates these models from the ``standard'' artificial neural networks
(ANN) where the frequency of spikes is replaced by real-valued signals. Spiking
neural P systems (SNPS) can be considered a branch of SNN based more on the
principles of formal automata, with many variants developed within the
framework of the membrane computing theory. In this paper, we first briefly
compare structure and function, advantages and drawbacks of SNN and SNPS. A key
part of the article is a survey of recent results and applications of machine
learning and deep learning models of both SNN and SNPS formalisms.
