Deep learning uses artificial neural networks to recognize patterns and learn from them to make decisions. Deep learning is a type of machine learning that uses artificial neural networks to mimic the human brain. It uses machine learning methods such as supervised, semi-supervised, or unsupervised learning strategies to learn automatically in deep architectures and has gained much popularity due to its superior ability to learn from huge amounts of data. It was found that deep learning approaches can be used for big data analysis successfully. Applications include virtual assistants such as Alexa and Siri, facial recognition, personalization, natural language processing, autonomous cars, automatic handwriting generation, news aggregation, the colorization of black and white images, the addition of sound to silent films, pixel restoration, and deep dreaming. As a review, this paper aims to categorically cover several widely used deep learning algorithms along with their architectures and their practical applications: backpropagation, autoencoders, variational autoencoders, restricted Boltzmann machines, deep belief networks, convolutional neural networks, recurrent neural networks, generative adversarial networks, capsnets, transformer, embeddings from language models, bidirectional encoder representations from transformers, and attention in natural language processing. In addition, challenges of deep learning are also presented in this paper, such as AutoML-Zero, neural architecture search, evolutionary deep learning, and others. The pros and cons of these algorithms and their applications in healthcare are explored, alongside the future direction of this domain. This paper presents a review and a checkpoint to systemize the popular algorithms and to encourage further innovation regarding their applications. For new researchers in the field of deep learning, this review can help them to obtain many details about the advantages, disadvantages, applications, and working mechanisms of a number of deep learning algorithms. In addition, we introduce detailed information on how to apply several deep learning algorithms in healthcare, such as in relation to the COVID-19 pandemic. By presenting many challenges of deep learning in one section, we hope to increase awareness of these challenges, and how they can be dealt with. This could also motivate researchers to find solutions for these challenges.