The increasing ubiquity of smartphones has led to the generation of vast amounts of data related to human activities. Human activity recognition is an important area of machine learning research as it has many applications, including entertainment, smart homes, smart environments, healthcare, security, etc. The research direction for HAR is shifting towards using smartphones because of their reliability in collecting and processing data independently using different embedded sensors. This paper displays the classification of HAR, sensors used in smartphones, classification of daily living activities, different approaches to machine learning techniques: traditional machine learning and deep learning (supervised and unsupervised), available datasets for HAR, and data processing for accurately classifying different human activities. Through an extensive literature review, this paper compares and displays many human activity recognition systems implemented on smartphone data or publicly available datasets using different sensors regarding the dataset used, classifiers, sensor used, advantages, disadvantages, and recognition accuracy in percentage. The paper also displays the comparisons of the best five papers in terms of author, year, dataset, algorithm and their accuracy, and the challenges of HAR.