As the failure of a bearing could cause cascading breakdowns of the mechanical system and then lead to costly repairs and production delays, bearing condition monitoring has received much attention for decades. One of the primary methods for this purpose is based on the analysis of vibration signal measured by accelerometers because such data are information-rich. The vibration signal collected from a defective bearing is, however, a mixture of several signal components including the fault-generated impulses, interferences from other machine components, and background noise, where fault-induced impulses are further modulated by various low frequency signal contents. The compounded effects of interferences, background noise and the combined modulation effects make it difficult to detect bearing faults. This is further complicated by the nonstationary nature of vibration signals due to speed variations in some cases, such as the bearings in a wind turbine. As such, the main challenges in the vibration-based bearing monitoring are how to address the modulation, noise, interference, and nonstationarity matters. Over the past few decades, considerable research activities have been carried out to deal with the first three issues. Recently, the nonstationarity matter has also attracted strong interests from both industry and academic community. Nevertheless, the existing techniques still have problems (deficiencies) as listed below: (1) The existing enveloping methods for bearing fault feature extraction are often adversely affected by multiple interferences. To eliminate the effect of interferences, the prefiltering is required, which is often parameter-dependent and knowledge-demanding. The selection of proper filter parameters is challenging and even more so in a time-varying environment. (2) Even though filters are properly designed, they are of little use in handling in-band noise and interferences which are also barriers for bearing fault detection, particularly for incipient bearing faults with weak signatures. (3) Conventional approaches for bearing fault detection under constant speed are no longer applicable to the variable speed case because such speed fluctuations may cause “smearing” of the discrete frequencies in the frequency representation. Most current methods for rotating machinery condition monitoring under time-varying speed require signal resampling based on the shaft rotating frequency. For the bearing case, the shaft rotating frequency is, however, often unavailable as it is coupled with the instantaneous fault characteristic frequency (IFCF) by a fault characteristic coefficient (FCC) which cannot be determined without knowing the fault type. Additionally, the effectiveness of resampling-based methods is largely dependent on the accuracy of resampling procedure which, even if reliable, can complicate the entire fault detection process substantially. (4) Time-frequency analysis (TFA) has proved to be a powerful tool in analyzing nonstationary signal and moreover does not require resampling for bearing fault identification. However, the diffusion of time-frequency representation (TFR) along time and frequency axes caused by lack of energy concentration would handicap the application of the TFA. In fact, the reported TFA applications in bearing fault diagnosis are still very limited. To address the first two aforementioned problems, i.e., (1) and (2), for constant speed cases, two morphology-based methods are proposed to extract bearing fault feature without prefiltering. Another two methods are developed to specifically handle the remaining problems for the bearing fault detection under time-varying speed conditions. These methods are itemized as follows: (1) An efficient enveloping method based on signal Fractal Dimension (FD) for bearing fault feature extraction without prefiltering, (2) A signal decomposition technique based on oscillatory behaviors for noise reduction and interferences removal (including in-band ones), (3) A prefiltering-free and resampling-free approach for bearing fault diagnosis under variable speed condition via the joint application of FD-based envelope demodulation and generalized demodulation (GD), and (4) A combined dual-demodulation transform (DDT) and synchrosqueezing approach for TFR energy concentration level enhancement and bearing fault identification. With respect to constant speed cases, the FD-based enveloping method, where a short time Fractal dimension (STFD) transform is proposed, can suppress interferences and highlight the fault-induced impulsive signature by transforming the vibration signal into a STFD representation. Its effectiveness, however, deteriorates with the increased complexity of the interference frequencies, particularly for multiple interferences with high frequencies. As such, the second method, which isolates fault-induced transients from interferences and noise via oscillatory behavior analysis, is then developed to complement the FD-based enveloping approach. Both methods are independent of frequency information and free from prefiltering, hence eliminating the tedious process for filter parameter specification. The in-band vibration interferences can also be suppressed mainly by the second approach. For the nonstationary cases, a prefiltering-free and resampling-free strategy is developed via the joint application of STFD and GD, from which a resampling-free order spectrum can be derived. This order spectrum can effectively reveal not only the existence of a fault but also its location. However, the success of this method relies largely on an effective enveloping technique. To address this matter and at the same time to exploit the advantages of TFA in nonstationary signal analysis, a TFA technique, involving dual demodulations and an iterative process, is developed and innovatively applied to bearing fault identification. The proposed methods have been validated using both simulation and experimental data collected in our lab. The test results have shown that the first two methods can effectively extract fault signatures, remove the interferences (including in-band ones) without prefiltering, and detect fault types from vibration signals for constant speed cases. The last two have shown to be effective in detecting faults and discern fault types from vibration data collected under variable speed conditions without resampling and prefiltering.