After providing an overview of solar activity as measured by the sunspot number (SSN) and space weather events during solar cycles (SCs) 21-24, we focus on the weak solar activity in SC 24. The weak solar activity reduces the number of energetic eruptions from the Sun and hence the number of space weather events. The speeds of coronal mass ejections (CMEs), interplanetary (IP) shocks, and the background solar wind all declined in SC 24. One of the main heliospheric consequences of weak solar activity is the reduced total (magnetic + gas) pressure, magnetic field strength, and Alfvén speed. There are three groups of phenomena that decline to different degrees in SC 24 relative to the corresponding ones in SC 23: (i) those that decline more than SSN does, (ii) those that decline like SSN, and (iii) those that decline less than SSN does. The decrease in the number of severe space weather events such as high-energy solar energetic particle (SEP) events and intense geomagnetic storms is deeper than the decline in SSN. The reduction in the number of severe space weather events can be explained by the backreaction of the weak heliosphere on CMEs. CMEs expand anomalously and hence their magnetic content is diluted resulting in weaker geomagnetic storms. The reduction in the number of intense geomagnetic storms caused by corotating interaction regions is also drastic. The diminished heliospheric magnetic field in SC 24 reduces the efficiency of particle acceleration, resulting in fewer high-energy SEP events. The numbers of IP type II radio bursts, IP socks, and high-intensity energetic storm particle events closely follow the number of fast and wide CMEs (and approximately SSN) because all these phenomena are closely related to CME-driven shocks. The number of halo CMEs in SC 24 declines less than SSN does, mainly due to the weak heliospheric state. Phenomena such as IP CMEs and magnetic clouds related to frontside halos also do not decline significantly. The mild space weather is likely to continue in SC 25, whose strength has been predicted to be not too different from that of SC 24.