This article gives an overview on recent progress in the generation of isolated attosecond pulse and isolated half-cycle attosecond pulse. As an isolated attosecond pulse is preferred in the pump-probe experiments for the dynamics of electrons in atom, molecule, or solid, we focus on the isolated attosecond pulses generation from the intense laser pulses interaction with solid density plasma, which have higher intensity and narrower pulse width than that generated in the interaction of laser pulse with gas target. We have firstly discussed the physical mechanism of isolated attosecond pulse generation, such as polarization gating, two-color laser pulses, attosecond light houses, and capacitor target mechanism. In the polarization gating mechanism, we have discussed the physical mechanism that the higher-order harmonic efficiency decreases with the increase of ellipticity. Both the coherent synchrotron radiation mechanism and the relativistic oscillation mechanism can control the intensity of high-order harmonic generation by controlling ellipticity of the incident laser pulse. We also discussed other mechanism to enhance the isolated attosecond pulse bursts in detail. Secondly, we focus on the isolated half-cycle attosecond pulses, which can also be generated from the intense laser pulses interaction with solid density plasma by double foil target mechanism, gas-foil target mechanism, cascaded generation mechanism, microstructured target mechanism, and three-color laser pulse mechanism. The half-cycle attosecond pulses can be useful for probing ultrafast electron dynamics in matter via asymmetric manipulation. Accordingly we discussed the physcial mechanism, experimental feasibility, calibration measurement, and application prospect of half-cycle attosecond pulse in this article. The above mechanism can directly generate ultra-intense isolated attosecond pulses in the transmission direction without requiring extra filters and gating techniques. The dense electron sheet is crucial for the generation of intense attosecond pulses in different mechanisms, such as coherent wake emission (CWE), relativistic oscillating mirror (ROM) and coherent synchrotron emission (CSE). In this article, all the mechanism for half-cycle attosecond pulses generation can ensure only one electron sheet contributing to the transmitted radiation. We discuss the theoretical model of nanobunching of the electron sheet, which shows that the relativistic oscillation is crucial for the formation of electron sheet.