Using particle-in-cell simulation technique, we investigate the plasma and ionization asymmetry, higher harmonics generation, electron and ion energy distribution function in capacitive discharges excited by tailored waveforms. At a base frequency of 13.56 MHz, three different waveforms namely, sinusoidal, saw-tooth, and square are applied for a constant current density amplitude of 50 A/m2 and gas pressure of 5 mTorr. The simulation results show that the square waveform produces highest plasma density in the discharge, whereas maximum asymmetry is observed for plasma excited by sawtooth like waveform. Both square and sawtooth waveforms generate multiple beams of high-energy electrons from near to the expanding phase of the sheath edge and high-frequency modulations up to 100 MHz on the instantaneous sheath position. The electron energy distribution function depicts 3 electron temperature and highly elevated tail-end electrons for the square waveform in comparison to the sinusoidal and sawtooth waveform. The ion energy distribution function is bimodal at both powered and grounded electrodes with a large asymmetry and narrow type distribution in the case of sawtooth like waveform. These results suggest that the choice of the waveform is highly critical for achieving maximum asymmetry and plasma density simultaneously in the discharge.